Three students — Ava, Ben, and Cal — each play a different instrument: piano, drums, or guitar. Ava does not play drums. Cal does not play piano or drums. What instrument does each student play?
AAva: piano, Ben: drums, Cal: guitar
BAva: guitar, Ben: piano, Cal: drums
CAva: drums, Ben: guitar, Cal: piano
DAva: piano, Ben: guitar, Cal: drums
Start with Cal: he does not play piano or drums, so he must play guitar. Now Ava: she does not play drums, and guitar is taken by Cal, so she plays piano. That leaves drums for Ben. The answer is Ava: piano, Ben: drums, Cal: guitar. Each clue eliminates options until only one possibility remains — that is deductive reasoning.
Question 2 Multiple Choice
In a logic puzzle, if a clue says 'The person with the red hat is NOT sitting next to the person with the blue hat,' what logical tool are you using?
APattern recognition — looking for a repeating sequence
BNegation and elimination — ruling out arrangements where red and blue are adjacent
CMultiplication — calculating the number of possible arrangements
DEstimation — guessing which arrangement looks right
The clue uses negation ('is NOT') to eliminate certain arrangements. You take the logical tool of negation and apply it to narrow down possibilities. This is the core logic puzzle technique: each clue eliminates some options, and eventually only one valid arrangement remains.
Question 3 True / False
Logic puzzles can typically be solved by guessing and checking.
TTrue
FFalse
Answer: False
While guess-and-check can sometimes work for simple puzzles, it becomes impractical as puzzles grow more complex. A 4-person puzzle might have dozens of possible arrangements. Systematic deduction — using each clue to eliminate impossibilities — is far more reliable and efficient. The goal of logic puzzles is to practice this systematic approach, not to develop guessing skills.
Question 4 Short Answer
Why is it important to use ALL the clues in a logic puzzle, even ones that seem unhelpful at first?
Think about your answer, then reveal below.
Model answer: Every clue in a well-designed puzzle provides information, even if it is not immediately obvious how to use it. Some clues eliminate options (negation clues like 'X is not Y'). Some clues establish relationships ('X is next to Y'). Some clues only become useful after other clues have been applied. Skipping a clue means potentially missing an elimination that would simplify later steps. Logic puzzles are designed so that all clues together produce exactly one solution — each clue is necessary.
This lesson applies beyond puzzles. In mathematics, science, and real-world problem-solving, relevant information is not always obviously useful upfront. The discipline of considering all available evidence before drawing conclusions is a core reasoning skill.