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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-0047
5 points, difficulty 3 of 3Level 5–6not yet calibrated
On a 4 by 4 board, how many aligned squares of any size are there, counting 1 by 1, 2 by 2, 3 by 3 and 4 by 4?
CNT-12Counting by position (sliding window)also CNT-04, GEO-02
KA-0049
5 points, difficulty 3 of 3Level 5–6not yet calibrated
The numbers 1 to 9 are placed in a row in some order. Can every neighbouring pair add up to an odd number?
NUM-03Parity of numbers (odd/even behavior)also LOG-05, CNT-04
KA-0052
5 points, difficulty 3 of 3Level 5–6has a figurenot yet calibrated
A circle of radius 5 is drawn inside a square of side 10, touching all four sides. What fraction of the square is outside the circle, to the nearest tenth?
GEO-04Area by subtraction (shaded regions)also GEO-03, GEO-07
KA-0060
5 points, difficulty 3 of 3Level 5–6not yet calibrated
A and B are different digits. The two-digit number AB added to the two-digit number BA gives 132. What is A + B?
NUM-14Operation puzzles and cryptarithmsalso NUM-01, LOG-08
KA-0070
5 points, difficulty 3 of 3Level 5–6not yet calibrated
Five children sit in a row. Two of them are twins who insist on sitting next to each other. In how many orders can the five sit?
CNT-11Counting with restrictionsalso CNT-05
KA-0071
5 points, difficulty 3 of 3Level 5–6not yet calibrated
Five beads of five different colours are threaded on a circular bracelet. Two bracelets count as the same if one can be turned or flipped into the other. How many different bracelets are there?
CNT-16Overcount, then correctalso CNT-15, CNT-05
KA-0075
5 points, difficulty 3 of 3Level 5–6not yet calibrated
How many three-digit whole numbers contain at least one digit 7?
CNT-09Complementary countingalso CNT-03, NUM-01
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-0082
5 points, difficulty 3 of 3Level 5–6has a figurenot yet calibrated
A room is 8 m long, 4 m wide and 2 m high. An ant walks across the floor and the walls from one bottom corner to the far top corner. What is the shortest distance in metres?
GEO-17Shortest paths on and around shapesalso GEO-10, GEO-01
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-0094
5 points, difficulty 3 of 3Level 5–6not yet calibrated
One of nine identical-looking coins is slightly heavier. Using only a balance, what is the smallest number of weighings that is certain to find it?
LOG-10Weighing and balance puzzlesalso CNT-04, LOG-11

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