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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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39 problemsClear all filters

KA-0077
5 points, difficulty 3 of 3Level 5–6not yet calibrated
A box holds 4 red, 5 blue and 6 green balls, mixed up. How many must be taken out without looking to be sure of having 3 of the same colour?
CNT-17The pigeonhole principlealso CNT-18
KA-0078
5 points, difficulty 3 of 3Level 5–6not yet calibrated
Ten different whole numbers, each bigger than zero, add up to 100. What is the largest that the biggest of them can be?
CNT-18Extremal / worst-case countingalso LOG-11, NUM-08
KA-0090
5 points, difficulty 3 of 3Level 5–6not yet calibrated
A cube 3 units on each side is painted all over and then cut into unit cubes. How many of them have exactly two painted faces?
CNT-14Counting cubes in a stack, including hidden onesalso GEO-13, CNT-04
KA-0133
5 points, difficulty 3 of 3Level 3–4not yet calibrated
How many squares of any size can be found on a 3 by 3 board?
CNT-13Counting shapes hidden inside a figurealso CNT-12, CNT-04
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-0143
3 points, difficulty 1 of 3Level 5–6not yet calibrated
How many three-digit numbers can be written using only the digits 1 and 2, with repeats allowed?
CNT-01Systematic listingalso CNT-03, NUM-01
KA-0154
4 points, difficulty 2 of 3Level 7–8not yet calibrated
In a class of 30 students, 18 play football and 15 play chess. Exactly 7 students do both. How many students play neither?
CNT-10Inclusion–exclusion with two setsalso CNT-09, CFT-01
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-0163
4 points, difficulty 2 of 3Level 9–10not yet calibrated
A club has 8 members. In how many ways can a group of 3 be chosen to attend a conference, if the three places are all the same?
CNT-06Selections of a few objectsalso CNT-16, CFT-01
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-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-0172
4 points, difficulty 2 of 3Level 11–12not yet calibrated
A committee of 4 must be formed from 5 boys and 4 girls, and it must contain exactly 2 boys and 2 girls. How many different committees are possible?
CNT-06Selections of a few objectsalso CNT-04, CNT-16

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