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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

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4 pt
5 pt

Strand

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

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29 problemsClear all filters

KA-0025
5 points, difficulty 3 of 3Level 5–6not yet calibrated
Four beads - one red, one green, one blue, one yellow - are threaded on a circular bracelet. Two bracelets are the same if one can be rotated into the other. How many different bracelets are there?
CNT-15Counting up to symmetryalso CNT-05, GEO-08
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-0031
5 points, difficulty 3 of 3Level 5–6has a figurenot yet calibrated
On the street grid shown you may only walk right or down. One junction is closed. How many routes go from the top-left corner to the bottom-right corner?
CNT-07Counting paths on a gridalso CNT-03, GEO-02
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-0037
5 points, difficulty 3 of 3Level 5–6not yet calibrated
What is the units digit of 7 multiplied by itself 2026 times, that is 7 to the power 2026?
NUM-07Last-digit behavior of products and powersalso NUM-06, PAT-03
KA-0040
5 points, difficulty 3 of 3Level 5–6not yet calibrated
A drawer holds 10 red socks, 10 blue socks and 10 green socks, all mixed up in the dark. How many socks must you take out to be sure of having a matching pair?
CNT-17The pigeonhole principlealso CNT-18, LOG-09
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-0045
5 points, difficulty 3 of 3Level 5–6not yet calibrated
A number is 4 more than a third of itself. Which of the choices is that number?
CFT-04Back-solve from the answer choicesalso CFT-05, MOD-01
KA-0047
5 points, difficulty 3 of 3Level 5–6not yet calibrated
On a 4 by 4 board, how many aligned squares of any size are there, counting 1 by 1, 2 by 2, 3 by 3 and 4 by 4?
CNT-12Counting by position (sliding window)also CNT-04, GEO-02
KA-0049
5 points, difficulty 3 of 3Level 5–6not yet calibrated
The numbers 1 to 9 are placed in a row in some order. Can every neighbouring pair add up to an odd number?
NUM-03Parity of numbers (odd/even behavior)also LOG-05, CNT-04
KA-0052
5 points, difficulty 3 of 3Level 5–6has a figurenot yet calibrated
A circle of radius 5 is drawn inside a square of side 10, touching all four sides. What fraction of the square is outside the circle, to the nearest tenth?
GEO-04Area by subtraction (shaded regions)also GEO-03, GEO-07
KA-0060
5 points, difficulty 3 of 3Level 5–6not yet calibrated
A and B are different digits. The two-digit number AB added to the two-digit number BA gives 132. What is A + B?
NUM-14Operation puzzles and cryptarithmsalso NUM-01, LOG-08

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