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177 problems, every one written from scratch, every wrong answer carrying the mistake that produces it. 708 explanations in all.

Level

1–2
3–4
5–6
7–8
9–10
11–12

Point value

3 pt
4 pt
5 pt

Strand

NUMNumber & Arithmetic
CNTCounting
GEOGeometry & Visualization
LOGLogic & Deduction
PATPatterns & Sequences
MODModeling & Word Problems
CFTContest Craft

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11 problemsClear all filters

KA-0028
5 points, difficulty 3 of 3Level 5–6not yet calibrated
Seven cups all stand upside down. In one move you must turn over exactly two cups. Can all seven ever stand the right way up?
LOG-05Parity argumentsalso NUM-03, LOG-09
KA-0034
5 points, difficulty 3 of 3Level 5–6has a figurenot yet calibrated
A 4 by 4 board has two opposite corner squares removed, leaving 14 squares. Each domino covers exactly two squares that share an edge. Can 7 dominoes cover the board?
LOG-07Coloring argumentsalso LOG-05, GEO-14
KA-0043
5 points, difficulty 3 of 3Level 5–6not yet calibrated
A bag holds 5 black and 6 white stones. You repeatedly remove two stones: if they match you put a black one in, if they differ you put a white one in. What colour is the last stone?
LOG-06Invariants and monovariantsalso LOG-05, NUM-03
KA-0092
4 points, difficulty 2 of 3Level 5–6not yet calibrated
Five children queue up. Ana is somewhere ahead of Bo. Cal is behind Bo but ahead of Dee. Eve is last. Who is second in the queue?
LOG-04Ordering and ranking from cluesalso LOG-01, CFT-02
KA-0094
5 points, difficulty 3 of 3Level 5–6not yet calibrated
One of nine identical-looking coins is slightly heavier. Using only a balance, what is the smallest number of weighings that is certain to find it?
LOG-10Weighing and balance puzzlesalso CNT-04, LOG-11
KA-0095
5 points, difficulty 3 of 3Level 5–6not yet calibrated
One hundred apples are packed into twelve boxes. What is the largest number n for which you can always be sure that some box holds at least n apples?
LOG-11The extremal principlealso CNT-17, NUM-15
KA-0097
5 points, difficulty 3 of 3Level 5–6not yet calibrated
The numbers 1 to 10 stand in a row. A move swaps two neighbours. After exactly 45 moves, can the row be back in its starting order?
LOG-05Parity argumentsalso NUM-03, LOG-06
KA-0098
5 points, difficulty 3 of 3Level 5–6not yet calibrated
The numbers 1 to 8 are on a board. A move rubs out two of them and writes their difference, larger minus smaller. After seven moves one number is left. Can it be 1?
LOG-06Invariants and monovariantsalso LOG-05, NUM-03
KA-0100
4 points, difficulty 2 of 3Level 5–6not yet calibrated
A number is doubled, then 6 is added, then the result is halved. The answer is 11. What was the original number?
LOG-08Working backwardsalso MOD-01
KA-0101
5 points, difficulty 3 of 3Level 5–6not yet calibrated
Can a 10 by 10 board be covered exactly by T-shaped tiles of four squares each, with no gaps and no overlaps?
LOG-07Coloring argumentsalso GEO-14, LOG-09
KA-0146
3 points, difficulty 1 of 3Level 5–6not yet calibrated
Suppose it is true that some birds cannot fly. Which of these must also be true?
LOG-01Reading a logical statement preciselyalso LOG-09