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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-0095
5 points, difficulty 3 of 3Level 5–6not yet calibrated
One hundred apples are packed into twelve boxes. What is the largest number n for which you can always be sure that some box holds at least n apples?
LOG-11The extremal principlealso CNT-17, NUM-15
KA-0097
5 points, difficulty 3 of 3Level 5–6not yet calibrated
The numbers 1 to 10 stand in a row. A move swaps two neighbours. After exactly 45 moves, can the row be back in its starting order?
LOG-05Parity argumentsalso NUM-03, LOG-06
KA-0098
5 points, difficulty 3 of 3Level 5–6not yet calibrated
The numbers 1 to 8 are on a board. A move rubs out two of them and writes their difference, larger minus smaller. After seven moves one number is left. Can it be 1?
LOG-06Invariants and monovariantsalso LOG-05, NUM-03
KA-0101
5 points, difficulty 3 of 3Level 5–6not yet calibrated
Can a 10 by 10 board be covered exactly by T-shaped tiles of four squares each, with no gaps and no overlaps?
LOG-07Coloring argumentsalso GEO-14, LOG-09
KA-0106
5 points, difficulty 3 of 3Level 5–6not yet calibrated
A machine turns 3 into 7, 5 into 11 and 8 into 17. What does it turn 12 into?
PAT-07Inferring a rule from examplesalso PAT-05, CFT-03
KA-0112
5 points, difficulty 3 of 3Level 5–6not yet calibrated
A class of 12 scored an average of 8. Another class of 18 scored an average of 13. What is the average for all 30 students together?
MOD-08Mixtures and weighted averagesalso NUM-15, NUM-11
KA-0125
5 points, difficulty 3 of 3Level 5–6not yet calibrated
What is the value of (1 - 1/2) x (1 - 1/3) x (1 - 1/4) x ... x (1 - 1/10)?
CFT-07Spot the trick vs. decide to grindalso NUM-09, CFT-03
KA-0126
5 points, difficulty 3 of 3Level 5–6not yet calibrated
You are 20 minutes into a 75-minute paper of 30 questions, still on question 9, and four minutes in with no progress. What is the best move?
CFT-08Time triage: now, later, or guessalso CFT-09, CFT-12
KA-0130
5 points, difficulty 3 of 3Level 5–6not yet calibrated
You reach the ten 5-point questions with 18 minutes left. What is the best plan?
CFT-12Managing the 5-point blockalso CFT-08, CFT-09
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-0134
5 points, difficulty 3 of 3Level 3–4not yet calibrated
A square sheet is folded in half, then in half again. Two holes are punched through all the layers. How many holes are there when it is unfolded?
GEO-15Paper folding and hole punchingalso GEO-09, CNT-03
KA-0135
5 points, difficulty 3 of 3Level 3–4not yet calibrated
How many two-digit numbers have both of their digits odd?
NUM-02Digit-constraint puzzlesalso NUM-03, CNT-03

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