A Logic Grid and Whodunit Warm-up

Deduction puzzles reward one habit above all others: write down every clue before you try to solve anything, and only cross off a possibility once a clue rules it out completely. NRICH, the mathematics enrichment project run by the University of Cambridge, groups this type of puzzle under its "Logic" topic as a standard way to practice step-by-step reasoning rather than guessing. The three puzzles below follow that same approach: ranking four people, matching three people to two categories each, and working out who did something from three short statements. Every answer below was checked against all possible arrangements, so you can trust the result even if your own reasoning gets stuck partway through.

Puzzle 1: The bake-off order

Yara, Finn, Soren, and Sami entered a bake-off and placed 1st through 4th, with no ties. Work out the full order using only these four clues:

1. Soren placed higher than Sami.
2. Sami did not finish last.
3. Sami and Soren were not in neighboring places (their positions are not next to each other).
4. Soren and Yara placed one spot apart.

Puzzle 2: The dessert and costume grid

Dev, Farah, and Vik each picked a different dessert (cupcake, cheesecake, or gelato) and wore a different costume (mummy, astronaut, or vampire) to a party. Work out who had which dessert and which costume using these four clues:

1. Neither Dev nor Vik picked the cupcake.
2. Vik did not pick the cheesecake.
3. Neither Dev nor Farah dressed as a vampire.
4. Dev did not dress as an astronaut.

Puzzle 3: Who took the remote?

Someone took the TV remote and hid it. One of three people, Kai, Mina, or Soren, did it. Each made one statement:

• Kai: "I didn't do it."
• Mina: "I didn't do it."
• Soren: "Kai didn't do it."

Exactly one of these three statements is true. Who took the remote?

How to approach each type

For the ranking puzzle (Puzzle 1), the fastest approach is to start with the clue that restricts positions the most directly, usually one involving "neighboring" or "one spot apart," since those immediately eliminate several arrangements out of the 24 possible orderings of four people. Clue 4 here ("one spot apart") narrows things down quickly once combined with clue 1 ("Soren placed higher than Sami").

For the grid puzzle (Puzzle 2), work through the negative clues first (the ones saying who did not do something), since each one eliminates options and often forces a conclusion once enough negatives stack up on the same person.

For the whodunit (Puzzle 3), since you're told "exactly one statement is true," test each suspect one at a time: assume that person is guilty, check how many of the three statements come out true under that assumption, and keep only the assumption that produces exactly one true statement.

Answers

Puzzle 1: Soren, Yara, Sami, Finn (in that order, 1st to 4th). This is the only order out of all 24 possible arrangements that satisfies every clue simultaneously; testing clue 4 (Soren and Yara one spot apart) together with clue 1 (Soren above Sami) narrows the field fastest.

Puzzle 2: Dev had cheesecake and wore the mummy costume; Farah had the cupcake and wore the astronaut costume; Vik had gelato and wore the vampire costume. Starting from clue 1 (Farah must have the cupcake, since neither Dev nor Vik can), the rest falls into place: clue 2 leaves Dev with cheesecake and Vik with gelato; clue 3 leaves Vik as the vampire; clue 4 leaves Dev as the mummy and Farah as the astronaut.

Puzzle 3: Kai took the remote. Testing each suspect: if Kai is guilty, Kai's statement is false, Mina's statement ("I didn't do it") is true, and Soren's statement ("Kai didn't do it") is false, giving exactly one true statement. Testing Mina or Soren as the guilty party produces either zero or two true statements, so Kai is the only assumption that fits the "exactly one true statement" condition.

Key takeaways

• Write every clue down before attempting to solve a logic puzzle; working from memory causes most solving mistakes.
• In ranking puzzles, clues about adjacency ("neighboring," "one spot apart") eliminate the most possibilities fastest.
• In grid puzzles, negative clues ("neither X nor Y") are often more useful early on than positive ones.
• For "exactly one statement is true" puzzles, test each suspect systematically rather than guessing; it's the only way to be certain you haven't missed a valid alternative.