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Number & Arithmetic15
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Logic & Deduction11
Patterns & Sequences7
Modeling & Word Problems10
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Code is MIT. Problems, skills, and explanations are CC BY-NC-SA 4.0. Practice never requires an account and nothing here is paywalled.

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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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177 problems

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-0160
3 points, difficulty 1 of 3Level 9–10not yet calibrated
A sequence begins 7, 11, 15, 19, and continues with the same constant step. What is the 30th term?
PAT-02Arithmetic sequences and the nth termalso MOD-01, CFT-10
KA-0161
3 points, difficulty 1 of 3Level 9–10not yet calibrated
What is the remainder when 2 to the power 50 is divided by 7?
NUM-06Remainders and modular cyclesalso NUM-07, PAT-03
KA-0162
3 points, difficulty 1 of 3Level 9–10not yet calibrated
Two towns are 300 km apart. A car leaves each town at the same moment driving toward the other, one at 60 km/h and the other at 90 km/h. How long until they meet?
MOD-03Rate, time, distancealso CFT-02, CFT-11
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-0164
4 points, difficulty 2 of 3Level 9–10not yet calibrated
Two triangles are similar. The sides of the smaller are 3/5 as long as the matching sides of the larger. The smaller triangle has area 18 square cm. What is the area of the larger triangle?
GEO-16Scaling and similar figuresalso NUM-11, CFT-11
KA-0165
4 points, difficulty 2 of 3Level 9–10not yet calibrated
Four litres of a solution that is 25 percent acid are mixed with six litres of a solution that is 50 percent acid. What percentage of the mixture is acid?
MOD-08Mixtures and weighted averagesalso NUM-10, CFT-10
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

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