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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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22 problemsClear all filters

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-0099
4 points, difficulty 2 of 3Level 3–4not yet calibrated
All the red boxes are heavy. Box X is not heavy. What must be true?
LOG-01Reading a logical statement preciselyalso LOG-09
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-0102
4 points, difficulty 2 of 3Level 3–4not yet calibrated
Cards numbered 1 to 10 lie face up. You take any six of them. Must two of your cards add up to 11?
LOG-09Informal proof by contradictionalso CNT-17, NUM-03
KA-0136
5 points, difficulty 3 of 3Level 3–4not yet calibrated
Four children stand in a line. Ana is not first. Bo stands directly behind Ana. Cal is last. Who is first?
LOG-04Ordering and ranking from cluesalso LOG-03, CFT-02
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
KA-0167
5 points, difficulty 3 of 3Level 9–10not yet calibrated
The numbers 1 to 10 are written on a board. You repeatedly rub out any two of them and write down their positive difference instead, until a single number is left. What can be said about that final number?
LOG-05Parity argumentsalso LOG-06, CFT-03
KA-0176
5 points, difficulty 3 of 3Level 11–12not yet calibrated
An 8 by 8 chessboard has two opposite corner squares removed, leaving 62 squares. Each domino covers exactly two squares that share an edge. Can the 62 squares be covered exactly by 31 dominoes?
LOG-07Coloring argumentsalso LOG-09, CNT-15

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