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177 problems, every one written from scratch, every wrong answer carrying the mistake that produces it. 708 explanations in all.

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9–10
11–12

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

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3 problemsClear all filters

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