Logic and number puzzles

1–20 of 36 matching questions · 36 in this version

• Three Heroes and Villains

  Identify which of three island inhabitants are truth-telling heroes and which are lying villains from their statements about one another. This exercises consistency checking across claims joined by “and” and “or,” with a label required for each person.

  rg-knights_knaves-0-0 · primary
• Three Saints and Sinners

  Classify three inhabitants as truth-telling saints or lying sinners using their linked statements. This exercises reasoning about “if” and “if and only if,” while keeping each speaker’s assigned role consistent with what they say.

  rg-knights_knaves-0-1 · primary
• Four Heroes with Linked Claims

  Determine the roles of four inhabitants whose statements combine direct claims, alternatives, and conditional relationships. The model must find a consistent hero-or-villain assignment and report a role for every person.

  rg-knights_knaves-1-0 · primary
• Four Saints with Nested Claims

  Assign saint or sinner roles to four people using a mix of direct accusations and nested logical statements. This tests whether the model can connect several claims without losing the rule that saints tell the truth and sinners lie.

  rg-knights_knaves-1-1 · primary
• Five Heroes with Nested Logic

  Classify five inhabitants as heroes or villains from statements containing nested “if and only if,” negation, and combined claims. This exercises tracking several interdependent truth conditions while producing a complete list of roles.

  rg-knights_knaves-2-0 · primary
• Five Sages and Fools

  Determine which of five inhabitants are truthful sages and which are lying fools. Their statements mix accusations, conditions, and negation, requiring the model to check that all assigned roles and statements fit together.

  rg-knights_knaves-2-1 · primary
• Three Houses with Drink Clues

  Use clues about three residents, their drinks, and their smoothies to identify who occupies the first house. This exercises combining neighbor relationships with fixed positions and unique attributes, returning only the requested name.

  rg-zebra_puzzles-0-0 · primary
• Three Houses with Pet Clues

  Identify the first house’s resident from clues linking three people to house positions, pets, and nationalities. This exercises elimination using unique assignments and direct facts, with only a single name requested.

  rg-zebra_puzzles-0-1 · primary
• Four Houses with Lunch Clues

  Work out who lives in the first of four houses using clues about colors, lunches, and pets. This exercises combining attribute matches with neighbor and immediately-left relationships while keeping every assignment unique.

  rg-zebra_puzzles-1-0 · primary
• Four Houses with Flower Clues

  Identify the first resident in a four-house row using flower, drink, and smoothie preferences. The model must combine linked preferences, fixed positions, and neighboring-house clues, then return only the resident’s name.

  rg-zebra_puzzles-1-1 · primary
• Five Houses with Phone Clues

  Find the first house’s resident among five people using clues about phones, pets, colors, and nationalities. This exercises keeping several sets of unique attributes aligned while applying fixed-position and immediately-left constraints.

  rg-zebra_puzzles-2-0 · primary
• Five Houses with Family Clues

  Identify who occupies the first of five houses from clues linking residents, nationalities, children, cigars, and pets. This exercises multi-step deduction across several attribute categories, including distinguishing residents’ names from children’s names.

  rg-zebra_puzzles-2-1 · primary
• Check Prerequisites for 11 Courses

  Decide whether all 11 courses can be completed under the listed prerequisites, returning True or False. This exercises following dependency chains and checking whether any circular requirement prevents a valid course order.

  rg-course_schedule-0-0 · primary
• Check Prerequisites for Eight Courses

  Determine whether eight courses can all be taken while respecting the supplied prerequisite pairs. The task exercises interpreting which course must come first and checking for circular dependencies, rather than producing a full schedule.

  rg-course_schedule-0-1 · primary
• Check Prerequisites for 17 Courses

  Check whether the prerequisite relationships among 17 courses permit completing them all. This exercises tracing indirect dependencies and detecting circular requirements, with a True-or-False answer rather than a proposed course sequence.

  rg-course_schedule-1-0 · primary
• Check Prerequisites for 18 Courses

  Decide whether all 18 courses can be completed given a list of prerequisite pairs. This exercises keeping dependency directions straight and checking whether linked requirements form a loop that blocks a valid ordering.

  rg-course_schedule-1-1 · primary
• Check Prerequisites for 26 Courses

  Evaluate whether the prerequisite list for 26 courses allows every course to be completed. This exercises tracking many interconnected requirements and checking for circular dependencies, then summarizing the conclusion as True or False.

  rg-course_schedule-2-0 · primary
• Check Prerequisites for 25 Courses

  Determine whether 25 courses can be arranged in an order that respects all supplied prerequisites. This exercises reasoning over direct and indirect dependencies; the requested output is only whether such an order is possible.

  rg-course_schedule-2-1 · primary
• Make 24 with a Repeated Pair

  Build an expression that makes 24 from four supplied numbers, including a repeated value, using each occurrence once. This exercises arithmetic search and number tracking, with only addition, subtraction, multiplication, and division allowed and an expression-only answer required.

  rg-puzzle24-0-0 · primary
• Make 24 with Three Repeats

  Make 24 from four supplied numbers, three of which share the same value, using each occurrence once. This exercises choosing arithmetic operations and grouping while respecting the available numbers and returning an expression rather than an equation.

  rg-puzzle24-0-1 · primary