Reasoning Gym Dataset Gallery

This gallery shows examples from all available datasets using their default configurations.

Available Datasets

base_conversion
basic_arithmetic
bf
caesar_cipher
chain_sum
color_cube_rotation
countdown
family_relationships
figlet_font
fraction_simplification
game_of_life
gcd
lcm
leg_counting
letter_counting
letter_jumble
maze
mini_sudoku
number_filtering
number_sequence
number_sorting
polynomial_equations
prime_factorization
propositional_logic
quantum_lock
rubiks_cube
sentence_reordering
simple_equations
spell_backward
sudoku
syllogism
word_ladder
word_sequence_reversal
word_sorting

Dataset Examples

base_conversion

Generates base conversion tasks

Default configuration:

min_base = 2
max_base = 16
min_value = 0
max_value = 1000
seed = 42
size = 500

Example tasks:

Example 1:
Question: Convert the base-3 number 28e to binary
Answer: 1010001110
Metadata: {'decimal_value': 654, 'source_base': 3, 'target_base': 2, 'source_repr': '28e', 'target_repr': '1010001110'}

Example 2:
Question: Convert the base-6 number 27 to base-13 (use lowercase letters a-z for digits above 9)
Answer: 27
Metadata: {'decimal_value': 39, 'source_base': 6, 'target_base': 13, 'source_repr': '27', 'target_repr': '27'}

Example 3:
Question: Convert the base-10 number 1a2 to base-13 (use lowercase letters a-z for digits above 9)
Answer: 1a2
Metadata: {'decimal_value': 418, 'source_base': 10, 'target_base': 13, 'source_repr': '1a2', 'target_repr': '1a2'}

basic_arithmetic

Dataset that generates basic arithmetic tasks with configurable complexity

Default configuration:

min_terms = 2
max_terms = 6
min_digits = 1
max_digits = 4
operators = ('+', '-', '*', '/')
allow_parentheses = True
allow_negation = True
seed = 42
size = 500
format_style = simple
whitespace = single

Example tasks:

Example 1:
Question: -5 * -6 =
Answer: 30
Metadata: {'num_terms': 2, 'num_digits': 1, 'expression': '-5 * -6'}

Example 2:
Question: 965 / 5 =
Answer: 193
Metadata: {'num_terms': 2, 'num_digits': 3, 'expression': '965 / 5'}

Example 3:
Question: 0 + -2 + -4 * 0 * 3 =
Answer: -2
Metadata: {'num_terms': 5, 'num_digits': 1, 'expression': '0 + -2 + -4 * 0 * 3'}

bf

Generates BF tasks

Default configuration:

seed = 42
size = 500
difficulty = 1

Example tasks:

Example 1:
Question: This is a BF (Brainf*ck) computer program. What is the output? 

>[-]>[-]<>++++++++++[<+++++++++++>-]<+.-.+++++.--------------.+++++++++++++++.<
Answer: onset
Metadata: {'bfit_code': '\nint main() {\n    print("onset");\n}\n', 'bf_program': '>[-]>[-]<>++++++++++[<+++++++++++>-]<+.-.+++++.--------------.+++++++++++++++.<'}

Example 2:
Question: This is a BF (Brainf*ck) computer program. What is the output? 

>[-]>[-]<>++++++++[<++++++++++++++>-]<.-----------.+++++++++++++.---------------.+++++.<
Answer: perch
Metadata: {'bfit_code': '\nint main() {\n    print("perch");\n}\n', 'bf_program': '>[-]>[-]<>++++++++[<++++++++++++++>-]<.-----------.+++++++++++++.---------------.+++++.<'}

Example 3:
Question: This is a BF (Brainf*ck) computer program. What is the output? 

>[-]>[-]<>+++++++++[<+++++++++++++>-]<.-------.----------.+.+++++++++++++.<
Answer: under
Metadata: {'bfit_code': '\nint main() {\n    print("under");\n}\n', 'bf_program': '>[-]>[-]<>+++++++++[<+++++++++++++>-]<.-------.----------.+.+++++++++++++.<'}

caesar_cipher

Generates Caesar cipher encryption/decryption tasks

Default configuration:

delimiter = .
min_words = 3
max_words = 20
min_rotation = 1
max_rotation = 25
seed = 42
size = 500

Example tasks:

Example 1:
Question: Decrypt this Caesar cipher text: JNJUBUF ZPVS BTTPDJBUF XIPN J XBT DPNQMJNFOUJOH B NPNFOU BHP
Answer: IMITATE YOUR ASSOCIATE WHOM I WAS COMPLIMENTING A MOMENT AGO
Metadata: {'rotation': 1, 'cipher_text': 'JNJUBUF ZPVS BTTPDJBUF XIPN J XBT DPNQMJNFOUJOH B NPNFOU BHP', 'clear_text': 'IMITATE YOUR ASSOCIATE WHOM I WAS COMPLIMENTING A MOMENT AGO'}

Example 2:
Question: Decrypt this Caesar cipher text: PBSDJ XKZYVOYX CWSDR LYEQRD SD PYB K WOBO KXN YBSQSXKDON DOVOZRYXSM TYEBXKVSCW
Answer: FRITZ NAPOLEON SMITH BOUGHT IT FOR A MERE AND ORIGINATED TELEPHONIC JOURNALISM
Metadata: {'rotation': 10, 'cipher_text': 'PBSDJ XKZYVOYX CWSDR LYEQRD SD PYB K WOBO KXN YBSQSXKDON DOVOZRYXSM TYEBXKVSCW', 'clear_text': 'FRITZ NAPOLEON SMITH BOUGHT IT FOR A MERE AND ORIGINATED TELEPHONIC JOURNALISM'}

Example 3:
Question: Decrypt this Caesar cipher text: ZW PFLI JKFDRTY ZJ FLK FW ZK DLJK SV DVEUVU
Answer: IF YOUR STOMACH IS OUT OF IT MUST BE MENDED
Metadata: {'rotation': 17, 'cipher_text': 'ZW PFLI JKFDRTY ZJ FLK FW ZK DLJK SV DVEUVU', 'clear_text': 'IF YOUR STOMACH IS OUT OF IT MUST BE MENDED'}

chain_sum

Generates simple arithmetic tasks using only + and - operators

Default configuration:

min_terms = 2
max_terms = 6
min_digits = 1
max_digits = 4
allow_negation = False
seed = 42
size = 500

Example tasks:

Example 1:
Question: 4 + 3 =
Answer: 7
Metadata: {'num_terms': 2, 'num_digits': 1, 'expression': '4 + 3'}

Example 2:
Question: 812 + 880 =
Answer: 1692
Metadata: {'num_terms': 2, 'num_digits': 3, 'expression': '812 + 880'}

Example 3:
Question: 2 + 6 + 3 + 4 + 0 =
Answer: 15
Metadata: {'num_terms': 5, 'num_digits': 1, 'expression': '2 + 6 + 3 + 4 + 0'}

color_cube_rotation

Generates color cube rotation reasoning tasks

Default configuration:

min_rotations = 1
max_rotations = 3
seed = 42
size = 500

Example tasks:

Example 1:
Question: A cube has:
- a pink top side
- a gray right side
- a orange front side
- a purple left side
- a indigo back side
- a cyan bottom side

The cube is rotated so that the side which was before at the bottom is now at the top.

What is now the color of the back side of the cube?
Answer: orange
Metadata: {'initial_state': {'top': 'pink', 'right': 'gray', 'front': 'orange', 'left': 'purple', 'back': 'indigo', 'bottom': 'cyan'}, 'rotations': ['bottom'], 'target_side': 'back', 'num_rotations': 1}

Example 2:
Question: A cube has:
- a gray top side
- a brown right side
- a silver front side
- a red left side
- a purple back side
- a yellow bottom side

The cube is rotated so that the side which was before at the left is now at the top.

Next, the bottom side is rotated to become the top face.

After that the cube is turned to make the bottom face the top.

What is now the color of the left side of the cube?
Answer: yellow
Metadata: {'initial_state': {'top': 'gray', 'right': 'brown', 'front': 'silver', 'left': 'red', 'back': 'purple', 'bottom': 'yellow'}, 'rotations': ['left', 'bottom', 'bottom'], 'target_side': 'left', 'num_rotations': 3}

Example 3:
Question: A cube has:
- a orange top side
- a cyan right side
- a violet front side
- a pink left side
- a gray back side
- a gold bottom side

The cube is rotated so that the side which was before at the left is now at the top.

Now the cube is rotated to place its back side at the top.

Now the cube is rotated to place its bottom side at the top.

What is now the color of the left side of the cube?
Answer: gold
Metadata: {'initial_state': {'top': 'orange', 'right': 'cyan', 'front': 'violet', 'left': 'pink', 'back': 'gray', 'bottom': 'gold'}, 'rotations': ['left', 'back', 'bottom'], 'target_side': 'left', 'num_rotations': 3}

countdown

Generates Countdown Number Game tasks

Default configuration:

min_numbers = 4
max_numbers = 6
min_value = 1
max_value = 100
min_target = 100
max_target = 999
operators = ('+', '-', '*', '/')
shuffle = True
seed = 42
size = 500

Example tasks:

Example 1:
Question: Calculate 139 using the numbers 36, 29, 95, 32, 4, 15.
Each number may be used at most once.
Answer: 15 - 4 + 95 + 36 - 32 + 29
Metadata: {'numbers': [36, 29, 95, 32, 4, 15], 'target': 139, 'expression': '15 - 4 + 95 + 36 - 32 + 29'}

Example 2:
Question: Using the numbers 74, 48, 56, 66, create an expression that equals 132.
You can only use each number once.
Answer: 66 - 56 + 74 + 48
Metadata: {'numbers': [74, 48, 56, 66], 'target': 132, 'expression': '66 - 56 + 74 + 48'}

Example 3:
Question: Using the numbers 5, 41, 38, 81, 14, create an expression that equals 450.
You can only use each number once.
Answer: 41*14 - 81 - 38 - 5
Metadata: {'numbers': [5, 41, 38, 81, 14], 'target': 450, 'expression': '41*14 - 81 - 38 - 5'}

family_relationships

Generates family relationship reasoning tasks

Default configuration:

min_family_size = 4
max_family_size = 8
male_names = ['James', 'John', 'Robert', 'Michael', 'William', 'David', 'Richard', 'Joseph', 'Thomas', 'Charles', 'Peter', 'Daniel', 'Matthew', 'Christopher', 'Andrew', 'George', 'Edward', 'Benjamin', 'Henry', 'Samuel', 'Alexander', 'Oliver', 'Jack', 'Harry', 'Jacob', 'Noah', 'Ethan', 'Lucas', 'Mason', 'Logan', 'Sebastian', 'Theodore', 'Owen', 'Liam', 'Aiden', 'Kai', 'Jayden', 'Zion', 'Phoenix', 'Atlas', 'Axel', 'Ryder', 'Finn']
female_names = ['Mary', 'Patricia', 'Jennifer', 'Linda', 'Elizabeth', 'Barbara', 'Susan', 'Jessica', 'Sarah', 'Karen', 'Emma', 'Lisa', 'Anna', 'Margaret', 'Victoria', 'Charlotte', 'Sophia', 'Isabella', 'Olivia', 'Ava', 'Mia', 'Emily', 'Abigail', 'Amelia', 'Eleanor', 'Grace', 'Alice', 'Lucy', 'Chloe', 'Sophie', 'Lily', 'Hannah', 'Zoe', 'Luna', 'Nova', 'Aria', 'Willow', 'Aurora', 'Sage', 'River', 'Winter', 'Sky', 'Rain']
seed = 42
size = 500

Example tasks:

Example 1:
Question: John is married to Isabella. They have a child called Edward. Edward is married to Victoria.

What is Isabella to Edward?
Answer: mother
Metadata: {'person1': 'Isabella', 'person2': 'Edward', 'relationship': 'mother', 'family_size': 4}

Example 2:
Question: Henry is married to Karen. They have a child called Sebastian. Sebastian is married to Eleanor.

What relation is Henry to Karen?
Answer: husband
Metadata: {'person1': 'Henry', 'person2': 'Karen', 'relationship': 'husband', 'family_size': 4}

Example 3:
Question: Liam is married to Nova. They have a child called Noah. Noah is married to Charlotte. They have a child called Patricia. Joseph is married to Lisa. They have a child called Charlotte.

What is Liam to Noah?
Answer: father
Metadata: {'person1': 'Liam', 'person2': 'Noah', 'relationship': 'father', 'family_size': 7}

figlet_font

Generates FigletFont tasks

Default configuration:

static_word = None
static_font = None
space_letters = True
seed = 42
size = 500

Example tasks:

Example 1:
Question: Please read the following figlet font:

  sSSSs        d s  b        sss.      d sss        sss sssss 
 S     S       S  S S      d           S                S     
S       S      S   SS      Y           S                S     
S       S      S    S        ss.       S sSSs           S     
S       S      S    S           b      S                S     
 S     S       S    S           P      S                S     
  "sss"        P    P      ` ss'       P sSSss          P     
                                                              

Answer: ONSET
Metadata: {'font': 'amc_tubes', 'space_letters': True}

Example 2:
Question: What word does this say?

######   ######   ######     ####   ##    ## 
 ##  ##   ##  ##   ##  ##   ##  ##   ##  ##  
 ##  ##   ##       ##  ##  ##   ##   ##  ##  
 #####    ####     #####   ##        ######  
 ##       ##       ## ##   ##   ##   ##  ##  
 ##       ##  ##   ## ##    ##  ##   ##  ##  
####     ######   ### ###    ####   ##    ## 
                                             

Answer: PERCH
Metadata: {'font': 'demo_2__', 'space_letters': True}

Example 3:
Question: What word does this say?

                                              
                                              
                                              
### ###   ### ###   #####    ######   #####   
 ## ##     ##  #     ## ##    ##  #    ## ##  
 ## ##     ### #     ## ##    ####     ## ##  
 ## ##     #####     ## ##    ##       ####   
 ## ##     ## ##     ## ##    ## ##    ## ##  
  ###     ### ##    #####    ######   #### ## 
                                              
                                              

Answer: UNDER
Metadata: {'font': 'xcourb', 'space_letters': True}

fraction_simplification

Generates fraction simplification tasks

Default configuration:

min_value = 1
max_value = 1000
min_factor = 1
max_factor = 100
styles = ('plain', 'latex_inline', 'latex_frac', 'latex_dfrac')
seed = 42
size = 500

Example tasks:

Example 1:
Question: Simplify the fraction $\frac{92}{524}$ to its lowest terms
Answer: $\frac{23}{131}$
Metadata: {'numerator': 92, 'denominator': 524, 'simplified_numerator': 23, 'simplified_denominator': 131, 'reduction_factor': 4, 'style': 'latex_frac'}

Example 2:
Question: Simplify the fraction $3600/26370$ to its lowest terms
Answer: $40/293$
Metadata: {'numerator': 3600, 'denominator': 26370, 'simplified_numerator': 40, 'simplified_denominator': 293, 'reduction_factor': 90, 'style': 'latex_inline'}

Example 3:
Question: Simplify the fraction 29330/37310 to its lowest terms
Answer: 419/533
Metadata: {'numerator': 29330, 'denominator': 37310, 'simplified_numerator': 419, 'simplified_denominator': 533, 'reduction_factor': 70, 'style': 'plain'}

game_of_life

Generates Game of Life games with configurable parameters

Default configuration:

grid_size_x = 20
grid_size_y = 20
filled_cells = 100
simulation_steps = 1
seed = 42
size = 500

Example tasks:

Example 1:
Question: What will this Game of Life board look like after 1 steps of simulation?

[[0 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0]
 [0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0]
 [0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 0]
 [1 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0 1 0 0]
 [0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 1 0 0 0]
 [0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 0 0 1 0 0]
 [0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0]
 [1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0]
 [1 1 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0]
 [0 0 1 0 0 0 0 1 0 0 0 0 1 1 0 0 1 0 0 1]
 [1 1 0 1 0 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0]
 [0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 1 1]
 [0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1]
 [0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1]
 [0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0]
 [1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0]
 [1 0 0 1 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1]
 [0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0]
 [0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0]
 [0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0]]
Answer: [[0 0 1 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0]
 [0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0]
 [0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 1 0]
 [0 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0 1 1 0]
 [0 0 0 0 0 1 1 1 0 0 1 1 0 1 0 0 1 1 0 0]
 [0 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 1 1 1 0]
 [0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1]
 [1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0]
 [0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0]
 [0 0 0 0 0 0 1 1 1 0 0 0 1 1 0 0 0 0 0 1]
 [1 1 1 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 1 0]
 [0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 1]
 [0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1]
 [1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1]
 [1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1]
 [1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0]
 [1 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1]
 [0 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0]
 [0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
 [0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]]
Metadata: {'grid_size_x': 20, 'grid_size_y': 20, 'filled_cells': 100, 'simulation_steps': 1}

Example 2:
Question: What will this Game of Life board look like after 1 steps of simulation?

[[1 0 0 1 0 1 1 0 0 0 1 0 0 0 0 0 1 0 0 0]
 [0 0 1 1 1 1 0 0 0 1 0 0 0 0 0 1 0 0 1 0]
 [0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 0 0]
 [0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 1 1 1]
 [0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0]
 [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0]
 [0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0]
 [1 1 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0]
 [0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0]
 [0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0]
 [0 1 0 0 1 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0]
 [0 0 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1]
 [0 0 1 1 1 1 0 0 1 0 0 1 1 0 0 0 0 0 0 1]
 [0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1]
 [0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 1 1]
 [0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1]
 [0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0]
 [0 0 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1]
 [0 1 0 0 1 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0]
 [0 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0]]
Answer: [[0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 1]
 [0 0 1 1 0 1 1 0 0 1 1 0 0 0 0 1 0 1 0 0]
 [0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 1 0 0 1]
 [0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1]
 [0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1]
 [0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
 [1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
 [1 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0]
 [0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0]
 [0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0]
 [0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
 [1 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0 0 0 0]
 [1 0 1 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 1]
 [1 0 1 1 0 1 0 0 0 1 1 0 0 0 0 0 0 1 0 0]
 [1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0]
 [0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1]
 [0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
 [0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
 [0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0]
 [0 1 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]]
Metadata: {'grid_size_x': 20, 'grid_size_y': 20, 'filled_cells': 100, 'simulation_steps': 1}

Example 3:
Question: What will this Game of Life board look like after 1 steps of simulation?

[[0 0 1 1 0 0 0 1 0 0 1 0 0 1 0 0 0 0 1 1]
 [0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 0 0 0 0 1]
 [0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0]
 [0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 1 0]
 [0 0 1 0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0]
 [0 0 0 1 1 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0]
 [0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0]
 [0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 1 0 1]
 [0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0]
 [1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1]
 [0 0 0 1 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0]
 [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0]
 [0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0]
 [0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0]
 [0 0 1 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 1 0]
 [0 0 1 1 1 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0]
 [0 0 1 1 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0]
 [1 0 0 1 1 0 1 0 0 1 0 0 0 0 0 1 1 0 0 0]
 [0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0]
 [0 1 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0]]
Answer: [[1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1]
 [0 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0 0 0 1 1]
 [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
 [0 0 0 1 1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0]
 [0 0 0 0 1 1 1 1 1 0 0 1 1 0 0 0 0 0 0 0]
 [0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
 [0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 1 0 0 0]
 [0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0]
 [0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1]
 [0 1 1 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0]
 [0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1]
 [0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0]
 [0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0]
 [0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 1 0 0]
 [0 0 1 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0]
 [0 1 0 0 1 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0]
 [0 1 0 0 0 0 0 0 1 0 1 0 0 0 1 0 1 0 0 0]
 [0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0]
 [0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 0 0]
 [0 0 0 0 1 0 0 0 0 0 1 1 1 0 0 0 0 0 1 0]]
Metadata: {'grid_size_x': 20, 'grid_size_y': 20, 'filled_cells': 100, 'simulation_steps': 1}

gcd

Generates Greatest Common Divisor (GCD) tasks

Default configuration:

min_numbers = 2
max_numbers = 2
min_value = 1
max_value = 1000
seed = 42
size = 500

Example tasks:

Example 1:
Question: Find the Greatest Common Divisor (GCD) of these numbers: 26, 760
Answer: 2
Metadata: {'numbers': [26, 760], 'result': 2}

Example 2:
Question: Find the Greatest Common Divisor (GCD) of these numbers: 688, 716
Answer: 4
Metadata: {'numbers': [688, 716], 'result': 4}

Example 3:
Question: Find the Greatest Common Divisor (GCD) of these numbers: 297, 30
Answer: 3
Metadata: {'numbers': [297, 30], 'result': 3}

lcm

Generates Least Common Multiple (LCM) tasks

Default configuration:

min_numbers = 2
max_numbers = 2
min_value = 1
max_value = 100
seed = 42
size = 500

Example tasks:

Example 1:
Question: Find the Least Common Multiple (LCM) of these numbers: 95, 14
Answer: 1330
Metadata: {'numbers': [95, 14], 'result': 1330}

Example 2:
Question: Find the Least Common Multiple (LCM) of these numbers: 60, 48
Answer: 240
Metadata: {'numbers': [60, 48], 'result': 240}

Example 3:
Question: Find the Least Common Multiple (LCM) of these numbers: 38, 4
Answer: 76
Metadata: {'numbers': [38, 4], 'result': 76}

leg_counting

Generates leg counting arithmetic tasks

Default configuration:

min_animals = 2
max_animals = 5
max_instances = 3
seed = 42
size = 500

Example tasks:

Example 1:
Question: How many legs are there in total if you have 1 sea slug, 1 deer?
Answer: 4
Metadata: {'animals': {'sea slug': 1, 'deer': 1}, 'total_legs': 4}

Example 2:
Question: How many legs are there in total if you have 2 sheeps, 2 dogs?
Answer: 16
Metadata: {'animals': {'sheep': 2, 'dog': 2}, 'total_legs': 16}

Example 3:
Question: How many legs are there in total if you have 1 crab, 2 lobsters, 1 human, 1 cow, 1 bee?
Answer: 42
Metadata: {'animals': {'crab': 1, 'lobster': 2, 'human': 1, 'cow': 1, 'bee': 1}, 'total_legs': 42}

letter_counting

Generates letter counting tasks from text spans

Default configuration:

min_words = 5
max_words = 15
seed = 42
size = 500

Example tasks:

Example 1:
Question: How many times does the letter "a" appear in the text: "bed and enters his mechanical dresser Two minutes later the machine deposited him all dressed"?
Answer: 6
Metadata: {'span_length': 15, 'target_letter': 'a', 'span': ['bed', 'and', 'enters', 'his', 'mechanical', 'dresser', 'Two', 'minutes', 'later', 'the', 'machine', 'deposited', 'him', 'all', 'dressed']}

Example 2:
Question: How many times does the letter "w" appear in the text: "it into a watering place"?
Answer: 1
Metadata: {'span_length': 5, 'target_letter': 'w', 'span': ['it', 'into', 'a', 'watering', 'place']}

Example 3:
Question: How many times does the letter "t" appear in the text: "readable form accessible by the widest array of equipment including outdated"?
Answer: 5
Metadata: {'span_length': 11, 'target_letter': 't', 'span': ['readable', 'form', 'accessible', 'by', 'the', 'widest', 'array', 'of', 'equipment', 'including', 'outdated']}

letter_jumble

Generates word letter jumbling tasks

Default configuration:

min_word_len = 1
max_word_len = 64
min_words = 3
max_words = 20
min_corruption_level = 0.1
max_corruption_level = 0.9
consecutive_words = True
seed = 42
size = 500

Example tasks:

Example 1:
Question: Unscramble these words: ew hsall eb ebla ot puodrce
Answer: we shall be able to produce
Metadata: {'num_words': 6, 'corruption_level': 0.12000860417813355, 'scrambled_words': ['ew', 'hsall', 'eb', 'ebla', 'ot', 'puodrce'], 'original_words': ['we', 'shall', 'be', 'able', 'to', 'produce']}

Example 2:
Question: Unscramble these words: ni oiurnalmsj Well Cahs
Answer: in journalism Well Cash
Metadata: {'num_words': 4, 'corruption_level': 0.3288673442377109, 'scrambled_words': ['ni', 'oiurnalmsj', 'Well', 'Cahs'], 'original_words': ['in', 'journalism', 'Well', 'Cash']}

Example 3:
Question: Unscramble these words: dear rchAdbali keep no nSice yrstyedae atnhks ot oyu rheet si a gain fo sucrbbisesr rM
Answer: dear Archibald keep on Since yesterday thanks to you there is a gain of subscribers Mr
Metadata: {'num_words': 16, 'corruption_level': 0.516016391169858, 'scrambled_words': ['dear', 'rchAdbali', 'keep', 'no', 'nSice', 'yrstyedae', 'atnhks', 'ot', 'oyu', 'rheet', 'si', 'a', 'gain', 'fo', 'sucrbbisesr', 'rM'], 'original_words': ['dear', 'Archibald', 'keep', 'on', 'Since', 'yesterday', 'thanks', 'to', 'you', 'there', 'is', 'a', 'gain', 'of', 'subscribers', 'Mr']}

maze

Generates mazes with guaranteed shortest path distance from start to goal within [min_dist, max_dist].

Default configuration:

min_dist = 5
max_dist = 10
min_grid_size = 5
max_grid_size = 10
seed = 42
size = 50

Example tasks:

Example 1:
Question: Navigate from '3' (start) to 'z' (goal):

```
>>>>>>>>>
>eeee>e>>
>ee>>>>>>
>eeeeee>>
>e>ee>>e>
>>ez>3e>>
>eee>e>e>
>eeeee>e>
>>>>>>>>>
```
Legend: '>' = Wall, 'e' = Passage

What is the minimum number of steps to reach the goal?
Answer: 6
Metadata: {'grid_size': 9, 'grid': ['>>>>>>>>>', '>eeee>e>>', '>ee>>>>>>', '>eeeeee>>', '>e>ee>>e>', '>>ez>3e>>', '>eee>e>e>', '>eeeee>e>', '>>>>>>>>>'], 'shortest_path_length': 6, 'start': '3', 'goal': 'z', 'wall': '>', 'path': 'e'}

Example 2:
Question: Navigate from '`' (start) to 'i' (goal):

```
4444444
4AAAAi4
4A4A4A4
4A4AA44
44AAAA4
44A`444
4444444
```
Legend: '4' = Wall, 'A' = Passage

What is the minimum number of steps to reach the goal?
Answer: 6
Metadata: {'grid_size': 7, 'grid': ['4444444', '4AAAAi4', '4A4A4A4', '4A4AA44', '44AAAA4', '44A`444', '4444444'], 'shortest_path_length': 6, 'start': '`', 'goal': 'i', 'wall': '4', 'path': 'A'}

Example 3:
Question: Navigate from '(' (start) to '`' (goal):

```
QQQQQQQ
QQ%%%%Q
QQ`%Q%Q
Q%%Q%%Q
Q%%%Q%Q
Q%QQ%(Q
QQQQQQQ
```
Legend: 'Q' = Wall, '%' = Passage

What is the minimum number of steps to reach the goal?
Answer: 8
Metadata: {'grid_size': 7, 'grid': ['QQQQQQQ', 'QQ%%%%Q', 'QQ`%Q%Q', 'Q%%Q%%Q', 'Q%%%Q%Q', 'Q%QQ%(Q', 'QQQQQQQ'], 'shortest_path_length': 8, 'start': '(', 'goal': '`', 'wall': 'Q', 'path': '%'}

mini_sudoku

Generates 4x4 sudoku puzzles with configurable difficulty

Default configuration:

min_empty = 8
max_empty = 12
seed = 42
size = 500

Example tasks:

Example 1:
Question: Solve this 4x4 Mini Sudoku puzzle:
_ _ _ _
_ _ _ _
_ 1 3 _
_ 4 _ 1
Answer: 4 2 1 3
1 3 4 2
2 1 3 4
3 4 2 1
Metadata: {'puzzle': [[0, 0, 0, 0], [0, 0, 0, 0], [0, 1, 3, 0], [0, 4, 0, 1]], 'solution': [[4, 2, 1, 3], [1, 3, 4, 2], [2, 1, 3, 4], [3, 4, 2, 1]], 'num_empty': 12}

Example 2:
Question: Solve this 4x4 Mini Sudoku puzzle:
3 _ _ _
_ _ 4 _
4 2 _ _
_ _ _ 4
Answer: 3 4 1 2
2 1 4 3
4 2 3 1
1 3 2 4
Metadata: {'puzzle': [[3, 0, 0, 0], [0, 0, 4, 0], [4, 2, 0, 0], [0, 0, 0, 4]], 'solution': [[3, 4, 1, 2], [2, 1, 4, 3], [4, 2, 3, 1], [1, 3, 2, 4]], 'num_empty': 11}

Example 3:
Question: Solve this 4x4 Mini Sudoku puzzle:
_ _ _ _
1 3 4 _
3 1 2 4
4 _ _ _
Answer: 2 4 1 3
1 3 4 2
3 1 2 4
4 2 3 1
Metadata: {'puzzle': [[0, 0, 0, 0], [1, 3, 4, 0], [3, 1, 2, 4], [4, 0, 0, 0]], 'solution': [[2, 4, 1, 3], [1, 3, 4, 2], [3, 1, 2, 4], [4, 2, 3, 1]], 'num_empty': 8}

number_filtering

Generates number filtering tasks

Default configuration:

min_numbers = 3
max_numbers = 10
min_decimals = 0
max_decimals = 4
min_value = -100.0
max_value = 100.0
seed = 42
size = 500

Example tasks:

Example 1:
Question: Keep all numbers larger than -90 in this list: ['-95.00', '-51.0', '47.2942', '-82.612']
Answer: ['-51.0', '47.2942', '-82.612']
Metadata: {'original_numbers': ['-95.00', '-51.0', '47.2942', '-82.612'], 'filter_value': '-90', 'operation': 'keep_larger', 'result': ['-51.0', '47.2942', '-82.612']}

Example 2:
Question: Remove all numbers larger than 18.236 in this list: ['-42.8', '91.88', '34']
Answer: ['-42.8']
Metadata: {'original_numbers': ['-42.8', '91.88', '34'], 'filter_value': '18.236', 'operation': 'remove_larger', 'result': ['-42.8']}

Example 3:
Question: Keep all numbers larger than 19.8962 in this list: ['4', '-64.7', '-42.1', '-77', '-79.9640', '37.76', '38.702', '18.20', '-28.34']
Answer: ['37.76', '38.702']
Metadata: {'original_numbers': ['4', '-64.7', '-42.1', '-77', '-79.9640', '37.76', '38.702', '18.20', '-28.34'], 'filter_value': '19.8962', 'operation': 'keep_larger', 'result': ['37.76', '38.702']}

number_sequence

Generates number sequence completion tasks with dynamic pattern generation

Default configuration:

min_terms = 4
max_terms = 8
min_value = -100
max_value = 100
max_complexity = 3
seed = 42
size = 500

Example tasks:

Example 1:
Question: 3, 6, 12, 24, 48, 96, 192, 384, ?
Answer: 768
Metadata: {'rule': 'double', 'complexity': 3, 'sequence': [3, 6, 12, 24, 48, 96, 192, 384, 768]}

Example 2:
Question: 8, 14, 20, 26, 32, 38, 44, ?
Answer: 50
Metadata: {'rule': 'add 6', 'complexity': 1, 'sequence': [8, 14, 20, 26, 32, 38, 44, 50]}

Example 3:
Question: 8, 4, 2, 1, 0, 0, 0, ?
Answer: 0
Metadata: {'rule': 'halve', 'complexity': 2, 'sequence': [8, 4, 2, 1, 0, 0, 0, 0]}

number_sorting

Generates number sorting tasks

Default configuration:

min_numbers = 3
max_numbers = 10
min_decimals = 0
max_decimals = 2
min_value = -100.0
max_value = 100.0
seed = 42
size = 500

Example tasks:

Example 1:
Question: Sort these numbers in ascending order: 48, -51, -72, -80
Answer: ['-80', '-72', '-51', '48']
Metadata: {'original_numbers': ['48', '-51', '-72', '-80'], 'direction': 'ascending', 'sorted_numbers': ['-80', '-72', '-51', '48']}

Example 2:
Question: Sort these numbers in ascending order: 39.2, -71.2, -7.5
Answer: ['-71.2', '-7.5', '39.2']
Metadata: {'original_numbers': ['39.2', '-71.2', '-7.5'], 'direction': 'ascending', 'sorted_numbers': ['-71.2', '-7.5', '39.2']}

Example 3:
Question: Sort these numbers in descending order: 8.39, 72.41, -64.67, -54.97, -94.18, -76.67, -98.24, -68.66, 2.74
Answer: ['72.41', '8.39', '2.74', '-54.97', '-64.67', '-68.66', '-76.67', '-94.18', '-98.24']
Metadata: {'original_numbers': ['8.39', '72.41', '-64.67', '-54.97', '-94.18', '-76.67', '-98.24', '-68.66', '2.74'], 'direction': 'descending', 'sorted_numbers': ['72.41', '8.39', '2.74', '-54.97', '-64.67', '-68.66', '-76.67', '-94.18', '-98.24']}

polynomial_equations

Generates random polynomial equations of degree in [min_degree, max_degree]. - The polynomial is formed by summing random terms of the form: coeff * x^exponent. - Then we solve "polynomial_expr = 0" using Sympy. - The solution may be real or complex; we filter real solutions by default for simplicity.

Default configuration:

min_terms = 2
max_terms = 4
min_value = 1
max_value = 100
min_degree = 1
max_degree = 3
operators = ('+', '-')
seed = 42
size = 500

Example tasks:

Example 1:
Question: Find the real value(s) of u in the equation: -127*u = 0
Answer: [0.0]
Metadata: {'polynomial_expr': '-127*u', 'variable': 'u', 'degree': 1, 'real_solutions': [0.0]}

Example 2:
Question: Determine the real value(s) of b tha satisfies: 86*b**2 - 2*b - 13 = 0
Answer: [-0.3773425275273891, 0.4005983414808775]
Metadata: {'polynomial_expr': '86*b**2 - 2*b - 13', 'variable': 'b', 'degree': 2, 'real_solutions': [-0.3773425275273891, 0.4005983414808775]}

Example 3:
Question: Determine the real value(s) of n tha satisfies: 71*n**3 - 2*n - 29 = 0
Answer: [0.7546129960163634]
Metadata: {'polynomial_expr': '71*n**3 - 2*n - 29', 'variable': 'n', 'degree': 3, 'real_solutions': [0.7546129960163634]}

prime_factorization

Generates prime factorization tasks

Default configuration:

min_value = 2
max_value = 1000
seed = 42
size = 500

Example tasks:

Example 1:
Question: Find the prime factorization of 656. Write the factors separated by × (Example: for 12 the answer would be: 2 × 2 × 3)
Answer: 2 × 2 × 2 × 2 × 41
Metadata: {'number': 656, 'factors': [2, 2, 2, 2, 41]}

Example 2:
Question: Find the prime factorization of 41. Write the factors separated by × (Example: for 12 the answer would be: 2 × 2 × 3)
Answer: 41
Metadata: {'number': 41, 'factors': [41]}

Example 3:
Question: Find the prime factorization of 420. Write the factors separated by × (Example: for 12 the answer would be: 2 × 2 × 3)
Answer: 2 × 2 × 3 × 5 × 7
Metadata: {'number': 420, 'factors': [2, 2, 3, 5, 7]}

propositional_logic

Generates propositional logic reasoning tasks

Default configuration:

min_vars = 2
max_vars = 4
min_statements = 2
max_statements = 4
max_complexity = 3
seed = 42
size = 500

Example tasks:

Example 1:
Question: Given:
1. R
2. Q
What can we conclude?
Answer: (P ∨ Q)
Metadata: {'premises': ['R', 'Q'], 'variables': ['P', 'Q', 'R', 'S'], 'complexity': 3}

Example 2:
Question: Given:
1. ((Q → P) ∨ (Q → P))
2. ((Q ↔ Q) → (P → P))
3. P
What can we conclude?
Answer: (P → P)
Metadata: {'premises': ['((Q → P) ∨ (Q → P))', '((Q ↔ Q) → (P → P))', 'P'], 'variables': ['P', 'Q'], 'complexity': 3}

Example 3:
Question: Given:
1. ((Q ∨ P) ∧ ¬P)
2. P
3. ((P ∧ R) ∧ ¬R)
4. ((Q ↔ R) → ¬Q)
What can we conclude?
Answer: (Q ∧ Q)
Metadata: {'premises': ['((Q ∨ P) ∧ ¬P)', 'P', '((P ∧ R) ∧ ¬R)', '((Q ↔ R) → ¬Q)'], 'variables': ['P', 'Q', 'R'], 'complexity': 3}

quantum_lock

Generates QuantumLock tasks

Default configuration:

difficulty = 10
seed = 42
size = 500

Example tasks:

Example 1:
Question: In front of you are some buttons, a light, and a number. The light will toggle between red and green whenever you press a button. Each button performs a mathematical operation to the number, but the operation may depend on the state of the light.
You must press the shortest correct sequence of buttons to reach the target value.

Start: 0 (red)
Target: 46
Buttons:
A: Add 3 (when any)
B: Add 2 (when any)
C: Multiply 2 (when any)
Answer: A → B → C → C → A → C
Metadata: {'difficulty': 10, 'solution_path': ['A', 'B', 'C', 'C', 'A', 'C'], 'target_value': 46, 'buttons': [{'name': 'A', 'type': 'add', 'value': 3, 'active_state': 'any'}, {'name': 'B', 'type': 'add', 'value': 2, 'active_state': 'any'}, {'name': 'C', 'type': 'multiply', 'value': 2, 'active_state': 'any'}], 'initial_state': 'red', 'initial_value': 0}

Example 2:
Question: In front of you are some buttons, a light, and a number. The light will toggle between red and green whenever you press a button. Each button performs a mathematical operation to the number, but the operation may depend on the state of the light.
You must press the shortest correct sequence of buttons to reach the target value.

Start: 0 (red)
Target: 30
Buttons:
A: Add 2 (when green)
B: Subtract 3 (when red)
C: Multiply 2 (when red)
Answer: C → A → C → A → C → A → C → A
Metadata: {'difficulty': 10, 'solution_path': ['C', 'A', 'C', 'A', 'C', 'A', 'C', 'A'], 'target_value': 30, 'buttons': [{'name': 'A', 'type': 'add', 'value': 2, 'active_state': 'green'}, {'name': 'B', 'type': 'subtract', 'value': 3, 'active_state': 'red'}, {'name': 'C', 'type': 'multiply', 'value': 2, 'active_state': 'red'}], 'initial_state': 'red', 'initial_value': 0}

Example 3:
Question: In front of you are some buttons, a light, and a number. The light will toggle between red and green whenever you press a button. Each button performs a mathematical operation to the number, but the operation may depend on the state of the light.
You must press the shortest correct sequence of buttons to reach the target value.

Start: 0 (red)
Target: 45
Buttons:
A: Subtract 2 (when any)
B: Add 3 (when any)
C: Add 2 (when any)
Answer: B → B → B → B → B → B → B → B → B → B → B → B → B → B → B
Metadata: {'difficulty': 10, 'solution_path': ['B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B'], 'target_value': 45, 'buttons': [{'name': 'A', 'type': 'subtract', 'value': 2, 'active_state': 'any'}, {'name': 'B', 'type': 'add', 'value': 3, 'active_state': 'any'}, {'name': 'C', 'type': 'add', 'value': 2, 'active_state': 'any'}], 'initial_state': 'red', 'initial_value': 0}

rubiks_cube

Generates RubiksCube tasks

Default configuration:

scramble_steps = 3
cube_size = 3
remove_ansi = True
seed = 42
size = 500

Example tasks:

Example 1:
Question: You are given a 3x3x3 Rubik's cube. It looks like this:

          G  Y  G                   
          G  Y  G                   
          G  R  G                   
 W  W  W  O  G  O  Y  Y  Y  R  B  R 
 R  R  R  W  G  W  O  O  O  Y  B  Y 
 R  R  R  W  G  W  O  O  O  Y  B  Y 
          B  O  B                   
          B  W  B                   
          B  W  B                   
 

Please provide a solution to solve this cube using Singmaster notation.
Answer: None
Metadata: {'cube_size': 3, 'scramble_steps': 3, 'scramble_moves': "F L' R", 'example_correct_answer': "L F' U' R D B' D' U R U' R' U B U' B' U' R' U R U B U' B' U R' U R U B U' B' U' B' U B U L U' L' U' B' U B U L U' L' U B' U B U L U' L' F R U R' U' F' U' R U R' U R U U R' F U' B' U F' U' B R' D' R D R' D' R D R' D' R D R' D' R D U R' D' R D R' D' R D U R' D' R D R' D' R D R' D' R D R' D' R D U R' D' R D R' D' R D U"}

Example 2:
Question: You are given a 3x3x3 Rubik's cube. It looks like this:

          Y  Y  R                   
          Y  Y  R                   
          G  G  R                   
 B  B  Y  R  R  B  W  W  W  G  O  O 
 R  R  W  G  G  G  Y  O  O  B  B  Y 
 R  R  W  G  G  G  Y  O  O  B  B  Y 
          O  O  O                   
          B  W  W                   
          B  W  W                   
 

Please provide a solution to solve this cube using Singmaster notation.
Answer: None
Metadata: {'cube_size': 3, 'scramble_steps': 3, 'scramble_moves': "L' F U'", 'example_correct_answer': "U' D' B D L' U' F D R' D' U' R U' R' F' U U F U F U' F' U' L' U L U F U' F' U L' U L U F U' F' R U' R' U' F' U F R' U R U B U' B' U' U' B' U B U L U' L' F R U R' U' R U R' U' F' U R U R' U R U U R' U' R U R' U R U U R' U' R U' L' U R' U' L U F U' B' U F' U' B R' D' R D R' D' R D U U R' D' R D R' D' R D U R' D' R D R' D' R D U"}

Example 3:
Question: You are given a 3x3x3 Rubik's cube. It looks like this:

          Y  Y  W                   
          Y  Y  W                   
          Y  Y  W                   
 G  G  G  O  O  B  O  O  O  G  R  R 
 R  R  R  G  G  B  O  O  O  G  B  B 
 R  R  R  G  G  R  B  B  B  O  B  B 
          W  W  Y                   
          W  W  Y                   
          W  W  Y                   
 

Please provide a solution to solve this cube using Singmaster notation.
Answer: None
Metadata: {'cube_size': 3, 'scramble_steps': 3, 'scramble_moves': "U R' R'", 'example_correct_answer': "R R U'"}

sentence_reordering

Generates sentence reordering tasks from text spans

Default configuration:

min_words_in_sentence = 3
max_words_in_sentence = 20
seed = 42
size = 500

Example tasks:

Example 1:
Question: Restore the correct order of words in the following sentence: wish could get I sleep. "I some
Answer: "I wish I could get some sleep.
Metadata: {'word_count': 7}

Example 2:
Question: Restore the correct order of words in the following sentence: the high level name. itself its unable it maintain at was of to Unfortunately,
Answer: Unfortunately, it was unable to maintain itself at the high level of its name.
Metadata: {'word_count': 14}

Example 3:
Question: Restore the correct order of words in the following sentence: developed by For the unutilized. energy falls ages went the
Answer: For ages the the energy developed by falls went unutilized.
Metadata: {'word_count': 10}

simple_equations

Generates simple equations with one variable to solve

Default configuration:

min_terms = 2
max_terms = 4
min_value = 1
max_value = 100
operators = ('+', '-', '*')
seed = 42
size = 500

Example tasks:

Example 1:
Question: Determine the value of u that satisfies: 32*u + 4 = 580
Answer: 18
Metadata: {'equation': '32*u + 4 = 580', 'variable': 'u'}

Example 2:
Question: Solve for b: 82080*b = 1067040
Answer: 13
Metadata: {'equation': '82080*b = 1067040', 'variable': 'b'}

Example 3:
Question: Determine the value of n that satisfies: 29*n - 5 = 430
Answer: 15
Metadata: {'equation': '29*n - 5 = 430', 'variable': 'n'}

spell_backward

Generates tasks to spell words backward

Default configuration:

min_word_len = 3
seed = 42
size = 500

Example tasks:

Example 1:
Question: Spell this word backward (example: sun -> nus): Project
Answer: tcejorP
Metadata: {'word': 'Project', 'word_len': 7}

Example 2:
Question: Spell this word backward (example: sun -> nus): Would
Answer: dluoW
Metadata: {'word': 'Would', 'word_len': 5}

Example 3:
Question: Spell this word backward (example: sun -> nus): One
Answer: enO
Metadata: {'word': 'One', 'word_len': 3}

sudoku

Generates sudoku puzzles with configurable difficulty

Default configuration:

min_empty = 30
max_empty = 50
seed = 42
size = 500

Example tasks:

Example 1:
Question: Solve this Sudoku puzzle:
4 _ _ _ 5 2 _ 3 _
_ _ 3 4 6 _ _ _ _
6 1 2 _ _ 8 4 _ _
1 _ _ _ _ _ 7 9 5
3 _ _ 7 1 _ _ 2 6
7 _ _ 5 _ _ _ _ 3
2 _ _ _ 7 5 _ _ _
_ 3 _ _ 4 1 _ _ _
_ _ _ 2 8 _ _ _ 4
Answer: 4 7 8 1 5 2 6 3 9
5 9 3 4 6 7 2 8 1
6 1 2 3 9 8 4 5 7
1 2 4 8 3 6 7 9 5
3 5 9 7 1 4 8 2 6
7 8 6 5 2 9 1 4 3
2 4 1 9 7 5 3 6 8
8 3 5 6 4 1 9 7 2
9 6 7 2 8 3 5 1 4
Metadata: {'puzzle': [[4, 0, 0, 0, 5, 2, 0, 3, 0], [0, 0, 3, 4, 6, 0, 0, 0, 0], [6, 1, 2, 0, 0, 8, 4, 0, 0], [1, 0, 0, 0, 0, 0, 7, 9, 5], [3, 0, 0, 7, 1, 0, 0, 2, 6], [7, 0, 0, 5, 0, 0, 0, 0, 3], [2, 0, 0, 0, 7, 5, 0, 0, 0], [0, 3, 0, 0, 4, 1, 0, 0, 0], [0, 0, 0, 2, 8, 0, 0, 0, 4]], 'solution': [[4, 7, 8, 1, 5, 2, 6, 3, 9], [5, 9, 3, 4, 6, 7, 2, 8, 1], [6, 1, 2, 3, 9, 8, 4, 5, 7], [1, 2, 4, 8, 3, 6, 7, 9, 5], [3, 5, 9, 7, 1, 4, 8, 2, 6], [7, 8, 6, 5, 2, 9, 1, 4, 3], [2, 4, 1, 9, 7, 5, 3, 6, 8], [8, 3, 5, 6, 4, 1, 9, 7, 2], [9, 6, 7, 2, 8, 3, 5, 1, 4]], 'num_empty': 48}

Example 2:
Question: Solve this Sudoku puzzle:
_ _ _ 1 3 2 6 4 5
_ 4 _ 7 _ _ _ 9 1
_ _ 1 8 _ 9 _ _ _
_ 8 9 _ _ _ 7 5 4
_ 3 _ 4 _ 1 9 8 _
4 6 _ 5 9 _ 1 2 3
5 _ 4 9 1 7 3 _ _
9 7 6 _ 8 4 5 1 _
8 _ 3 _ _ _ 4 7 _
Answer: 7 9 8 1 3 2 6 4 5
3 4 2 7 5 6 8 9 1
6 5 1 8 4 9 2 3 7
1 8 9 6 2 3 7 5 4
2 3 5 4 7 1 9 8 6
4 6 7 5 9 8 1 2 3
5 2 4 9 1 7 3 6 8
9 7 6 3 8 4 5 1 2
8 1 3 2 6 5 4 7 9
Metadata: {'puzzle': [[0, 0, 0, 1, 3, 2, 6, 4, 5], [0, 4, 0, 7, 0, 0, 0, 9, 1], [0, 0, 1, 8, 0, 9, 0, 0, 0], [0, 8, 9, 0, 0, 0, 7, 5, 4], [0, 3, 0, 4, 0, 1, 9, 8, 0], [4, 6, 0, 5, 9, 0, 1, 2, 3], [5, 0, 4, 9, 1, 7, 3, 0, 0], [9, 7, 6, 0, 8, 4, 5, 1, 0], [8, 0, 3, 0, 0, 0, 4, 7, 0]], 'solution': [[7, 9, 8, 1, 3, 2, 6, 4, 5], [3, 4, 2, 7, 5, 6, 8, 9, 1], [6, 5, 1, 8, 4, 9, 2, 3, 7], [1, 8, 9, 6, 2, 3, 7, 5, 4], [2, 3, 5, 4, 7, 1, 9, 8, 6], [4, 6, 7, 5, 9, 8, 1, 2, 3], [5, 2, 4, 9, 1, 7, 3, 6, 8], [9, 7, 6, 3, 8, 4, 5, 1, 2], [8, 1, 3, 2, 6, 5, 4, 7, 9]], 'num_empty': 34}

Example 3:
Question: Solve this Sudoku puzzle:
_ _ 1 2 3 _ _ _ 9
3 _ _ 1 8 5 6 7 2
_ _ _ 4 9 6 1 _ _
1 _ 5 7 _ _ 9 2 _
_ 4 _ _ 5 9 7 1 6
9 _ 6 _ 1 _ 4 5 3
_ _ 3 9 7 _ 2 8 4
_ _ 2 6 4 _ _ 9 1
_ 1 _ 5 2 8 3 _ _
Answer: 5 6 1 2 3 7 8 4 9
3 9 4 1 8 5 6 7 2
8 2 7 4 9 6 1 3 5
1 3 5 7 6 4 9 2 8
2 4 8 3 5 9 7 1 6
9 7 6 8 1 2 4 5 3
6 5 3 9 7 1 2 8 4
7 8 2 6 4 3 5 9 1
4 1 9 5 2 8 3 6 7
Metadata: {'puzzle': [[0, 0, 1, 2, 3, 0, 0, 0, 9], [3, 0, 0, 1, 8, 5, 6, 7, 2], [0, 0, 0, 4, 9, 6, 1, 0, 0], [1, 0, 5, 7, 0, 0, 9, 2, 0], [0, 4, 0, 0, 5, 9, 7, 1, 6], [9, 0, 6, 0, 1, 0, 4, 5, 3], [0, 0, 3, 9, 7, 0, 2, 8, 4], [0, 0, 2, 6, 4, 0, 0, 9, 1], [0, 1, 0, 5, 2, 8, 3, 0, 0]], 'solution': [[5, 6, 1, 2, 3, 7, 8, 4, 9], [3, 9, 4, 1, 8, 5, 6, 7, 2], [8, 2, 7, 4, 9, 6, 1, 3, 5], [1, 3, 5, 7, 6, 4, 9, 2, 8], [2, 4, 8, 3, 5, 9, 7, 1, 6], [9, 7, 6, 8, 1, 2, 4, 5, 3], [6, 5, 3, 9, 7, 1, 2, 8, 4], [7, 8, 2, 6, 4, 3, 5, 9, 1], [4, 1, 9, 5, 2, 8, 3, 6, 7]], 'num_empty': 33}

syllogism

Generates syllogism reasoning tasks

Default configuration:

terms = None
allow_all = True
allow_no = True
allow_some = True
allow_some_not = True
include_invalid = True
invalid_ratio = 0.3
seed = 42
size = 500

Example tasks:

Example 1:
Question: Consider these statements:
1. No students are humans
2. No humans are chefs

Does it logically follow that:
No students are chefs?
(Answer Yes or No)
Answer: Yes
Metadata: {'premise1': 'No students are humans', 'premise2': 'No humans are chefs', 'conclusion': 'No students are chefs', 'is_valid': True}

Example 2:
Question: Consider these statements:
1. Some ... are not children are animals
2. Some animals are doctors

Does it logically follow that:
All children are doctors?
(Answer Yes or No)
Answer: Yes
Metadata: {'premise1': 'Some ... are not children are animals', 'premise2': 'Some animals are doctors', 'conclusion': 'All children are doctors', 'is_valid': True}

Example 3:
Question: Consider these statements:
1. All butterflies are tigers
2. No tigers are whales

Does it logically follow that:
Some ... are not butterflies are whales?
(Answer Yes or No)
Answer: No
Metadata: {'premise1': 'All butterflies are tigers', 'premise2': 'No tigers are whales', 'conclusion': 'Some ... are not butterflies are whales', 'is_valid': False}

word_ladder

Generates word ladder transformation tasks

Default configuration:

min_word_length = 3
max_word_length = 5
min_chain_length = -1
max_chain_length = -1
seed = 42
size = 500

Example tasks:

Example 1:
Question: Transform the word 'CEILS' into 'ANIGH' by changing one letter at a time. Each step must create a valid English word (including plurals) and keep the same word length. Show the sequence of words needed.
Answer: CEILS,TEILS,TEINS,THINS,THIGS,THIGH,AHIGH,ANIGH
Metadata: {'start_word': 'CEILS', 'end_word': 'ANIGH', 'word_length': 5, 'chain_length': 8}

Example 2:
Question: Transform the word 'KAW' into 'EFS' by changing one letter at a time. Each step must create a valid English word (including plurals) and keep the same word length. Show the sequence of words needed.
Answer: KAW,KAS,EAS,EFS
Metadata: {'start_word': 'KAW', 'end_word': 'EFS', 'word_length': 3, 'chain_length': 4}

Example 3:
Question: Transform the word 'SAUT' into 'SKER' by changing one letter at a time. Each step must create a valid English word (including plurals) and keep the same word length. Show the sequence of words needed.
Answer: SAUT,SHUT,SHET,SKET,SKER
Metadata: {'start_word': 'SAUT', 'end_word': 'SKER', 'word_length': 4, 'chain_length': 5}

word_sequence_reversal

Generates word sequence reversal tasks from text spans

Default configuration:

min_words = 3
max_words = 8
seed = 42
size = 500

Example tasks:

Example 1:
Question: Reverse this list of words: bed, if, problem, but, Well, an, transmission, nutritive
Answer: nutritive, transmission, an, Well, but, problem, if, bed
Metadata: {'num_words': 8, 'words': ['bed', 'if', 'problem', 'but', 'Well', 'an', 'transmission', 'nutritive']}

Example 2:
Question: Reverse this list of words: it, pleasure, Gutenberg
Answer: Gutenberg, pleasure, it
Metadata: {'num_words': 3, 'words': ['it', 'pleasure', 'Gutenberg']}

Example 3:
Question: Reverse this list of words: readable, to, he, that, to, possession
Answer: possession, to, that, he, to, readable
Metadata: {'num_words': 6, 'words': ['readable', 'to', 'he', 'that', 'to', 'possession']}

word_sorting

Generates word sorting tasks

Default configuration:

min_words = 3
max_words = 10
min_word_length = 3
max_word_length = 12
transformation = original
seed = 42
size = 500

Example tasks:

Example 1:
Question: Sort these words in ascending order (using ASCII/Unicode ordering) and return them as a comma-separated list:
DIRECT, given, exclaims, dreaming
Answer: DIRECT, dreaming, exclaims, given
Metadata: {'original_words': ['DIRECT', 'given', 'exclaims', 'dreaming'], 'transformed_words': ['DIRECT', 'given', 'exclaims', 'dreaming'], 'direction': 'ascending', 'transformation': <TextTransformation.ORIGINAL: 'original'>, 'sorted_words': ['DIRECT', 'dreaming', 'exclaims', 'given']}

Example 2:
Question: Sort these words in descending order (using ASCII/Unicode ordering) and return them as a comma-separated list:
heat, begun, sometimes
Answer: sometimes, heat, begun
Metadata: {'original_words': ['heat', 'begun', 'sometimes'], 'transformed_words': ['heat', 'begun', 'sometimes'], 'direction': 'descending', 'transformation': <TextTransformation.ORIGINAL: 'original'>, 'sorted_words': ['sometimes', 'heat', 'begun']}

Example 3:
Question: Sort these words in ascending order (using ASCII/Unicode ordering) and return them as a comma-separated list:
violates, yes, already, completing, pages, duty, his, EXPRESS, duly
Answer: EXPRESS, already, completing, duly, duty, his, pages, violates, yes
Metadata: {'original_words': ['violates', 'yes', 'already', 'completing', 'pages', 'duty', 'his', 'EXPRESS', 'duly'], 'transformed_words': ['violates', 'yes', 'already', 'completing', 'pages', 'duty', 'his', 'EXPRESS', 'duly'], 'direction': 'ascending', 'transformation': <TextTransformation.ORIGINAL: 'original'>, 'sorted_words': ['EXPRESS', 'already', 'completing', 'duly', 'duty', 'his', 'pages', 'violates', 'yes']}

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Reasoning Gym Dataset Gallery

Available Datasets

Dataset Examples

base_conversion

basic_arithmetic

bf

caesar_cipher

chain_sum

color_cube_rotation

countdown

family_relationships

figlet_font

fraction_simplification

game_of_life

gcd

lcm

leg_counting

letter_counting

letter_jumble

maze

mini_sudoku

number_filtering

number_sequence

number_sorting

polynomial_equations

prime_factorization

propositional_logic

quantum_lock

rubiks_cube

sentence_reordering

simple_equations

spell_backward

sudoku

syllogism

word_ladder

word_sequence_reversal

word_sorting