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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-0007
4 points, difficulty 2 of 3Level 3–4not yet calibrated
Nadia gave half her stickers to her brother, then 6 more to a friend. She has 9 left. How many stickers did she start with?
LOG-08Working backwardsalso NUM-09
KA-0017
5 points, difficulty 3 of 3Level 3–4not yet calibrated
Ana says "Bo is lying." Bo says "Cal is lying." Cal says "Ana and Bo are both lying." How many of the three are telling the truth?
LOG-02Truth-tellers and liarsalso LOG-01, LOG-09
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-0050
3 points, difficulty 1 of 3Level 3–4not yet calibrated
Toma spent 4 euros, then spent half of what was left, and now has 6 euros. How much did she start with?
LOG-08Working backwardsalso MOD-06
KA-0091
4 points, difficulty 2 of 3Level 3–4not yet calibrated
Ana, Bo and Cal each keep a different pet: a cat, a dog and a fish. Ana does not keep the cat. Bo keeps neither the cat nor the fish. Who keeps the cat?
LOG-03Elimination gridsalso LOG-01
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-0093
4 points, difficulty 2 of 3Level 3–4not yet calibrated
Two apples balance three pears. One apple weighs 90 grams. How many grams does one pear weigh?
LOG-10Weighing and balance puzzlesalso NUM-11, MOD-01
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-0096
4 points, difficulty 2 of 3Level 3–4not yet calibrated
Ana says: "Bo and I are both liars." Each child is either always truthful or always a liar. Who is telling the truth?
LOG-02Truth-tellers and liarsalso LOG-09, LOG-01

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