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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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50 problemsClear all filters

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-0137
5 points, difficulty 3 of 3Level 3–4not yet calibrated
A jug holds 900 ml of juice. A third is poured out, then 150 ml is added. How many millilitres are in the jug?
MOD-10Multi-step arithmetic word problemsalso NUM-09, MOD-07
KA-0138
5 points, difficulty 3 of 3Level 3–4not yet calibrated
Squares of dots grow: 1 dot, then 4, then 9, then 16. How many dots are in the seventh square?
PAT-04Growth patterns and figurate numbersalso PAT-02, GEO-01
KA-0139
5 points, difficulty 3 of 3Level 3–4not yet calibrated
On a die, opposite faces add to 7. A die rests on a table with 3 on top. What do the four side faces add up to?
GEO-11Dice and cube face relationshipsalso NUM-08, CFT-05
KA-0140
5 points, difficulty 3 of 3Level 3–4not yet calibrated
A code uses the letters A, B and C, each exactly once. How many codes do not start with A?
CNT-03The multiplication principlealso CNT-11, CNT-09
KA-0157
5 points, difficulty 3 of 3Level 7–8not yet calibrated
A drawer holds 12 red socks, 10 blue socks and 8 green socks, all mixed up. You take socks out one at a time in the dark. What is the smallest number of socks you must take to be certain of having three of the same colour?
CNT-17The pigeonhole principlealso CNT-18, LOG-09
KA-0158
5 points, difficulty 3 of 3Level 7–8not yet calibrated
What is the last digit of 3 multiplied by itself 2026 times, that is, of 3 to the power 2026?
NUM-07Last-digit behavior of products and powersalso NUM-06, PAT-03
KA-0159
5 points, difficulty 3 of 3Level 7–8not yet calibrated
One tap fills a tank in 6 hours. A second tap fills the same tank in 4 hours. Both taps are opened together on an empty tank. How long does it take to fill?
MOD-04Combined work ratesalso NUM-09, CFT-11
KA-0166
5 points, difficulty 3 of 3Level 9–10not yet calibrated
Six friends sit around a circular table. Two seatings count as the same if one can be turned into the other by rotating the table. How many genuinely different seatings are there?
CNT-15Counting up to symmetryalso CNT-16, CNT-05
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-0168
5 points, difficulty 3 of 3Level 9–10not yet calibrated
An ordinary six-sided die is rolled three times. What is the probability that at least one roll shows a six?
CNT-09Complementary countingalso CNT-16, CFT-11
KA-0175
5 points, difficulty 3 of 3Level 11–12not yet calibrated
What is the smallest number n such that ANY collection of n whole numbers must contain two of them whose difference is divisible by 7?
CNT-17The pigeonhole principlealso NUM-06, LOG-09

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