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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-0025
5 points, difficulty 3 of 3Level 5–6not yet calibrated
Four beads - one red, one green, one blue, one yellow - are threaded on a circular bracelet. Two bracelets are the same if one can be rotated into the other. How many different bracelets are there?
CNT-15Counting up to symmetryalso CNT-05, GEO-08
KA-0026
3 points, difficulty 1 of 3Level 5–6not yet calibrated
A jacket costs 80 euros. Its price is reduced by 25%. What is the new price?
NUM-10Percentages and simple discountsalso NUM-09
KA-0027
4 points, difficulty 2 of 3Level 5–6has a figurenot yet calibrated
A square of side 10 has a smaller square of side 4 cut out of one corner. What is the area of the shape that remains?
GEO-04Area by subtraction (shaded regions)also GEO-01, GEO-03
KA-0028
5 points, difficulty 3 of 3Level 5–6not yet calibrated
Seven cups all stand upside down. In one move you must turn over exactly two cups. Can all seven ever stand the right way up?
LOG-05Parity argumentsalso NUM-03, LOG-09
KA-0029
3 points, difficulty 1 of 3Level 5–6not yet calibrated
A rope is 3.5 metres long. A second rope is 240 centimetres long. How much longer is the first rope, in centimetres?
MOD-07Unit conversionalso NUM-09
KA-0030
4 points, difficulty 2 of 3Level 5–6not yet calibrated
A sequence starts 4, 7, 10, 13 and continues in the same way. What is the 20th term?
PAT-02Arithmetic sequences and the nth termalso PAT-04
KA-0031
5 points, difficulty 3 of 3Level 5–6has a figurenot yet calibrated
On the street grid shown you may only walk right or down. One junction is closed. How many routes go from the top-left corner to the bottom-right corner?
CNT-07Counting paths on a gridalso CNT-03, GEO-02
KA-0032
3 points, difficulty 1 of 3Level 5–6has a figurenot yet calibrated
What is the angle between the hands of a clock at exactly 3 o'clock?
GEO-18Clock geometry: hands, angles, timesalso GEO-05
KA-0033
4 points, difficulty 2 of 3Level 5–6not yet calibrated
The mean of five numbers is 12. One of the numbers is removed and the mean of the remaining four is 11. What number was removed?
NUM-15Means, and working backwards from a meanalso LOG-08
KA-0034
5 points, difficulty 3 of 3Level 5–6has a figurenot yet calibrated
A 4 by 4 board has two opposite corner squares removed, leaving 14 squares. Each domino covers exactly two squares that share an edge. Can 7 dominoes cover the board?
LOG-07Coloring argumentsalso LOG-05, GEO-14
KA-0035
3 points, difficulty 1 of 3Level 5–6not yet calibrated
Eight people meet and everyone shakes hands with everyone else exactly once. How many handshakes take place?
CNT-08Handshakes and pairsalso CNT-06
KA-0036
4 points, difficulty 2 of 3Level 5–6not yet calibrated
Ravi cycles 12 km at 24 km per hour, then walks 6 km at 4 km per hour. How many minutes does the whole journey take?
MOD-03Rate, time, distancealso MOD-07

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