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Number & Arithmetic15
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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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39 problemsClear all filters

KA-0001
3 points, difficulty 1 of 3Level 3–4has a figurenot yet calibrated
A 3 by 3 board is drawn. How many 2 by 2 squares can be found on it, if they must line up with the grid?
CNT-12Counting by position (sliding window)also CNT-01
KA-0003
4 points, difficulty 2 of 3Level 3–4has a figurenot yet calibrated
A large triangle is cut by two lines from its top corner into three small triangles side by side. How many triangles of any size appear in the picture?
CNT-13Counting shapes hidden inside a figurealso CNT-04
KA-0009
4 points, difficulty 2 of 3Level 3–4has a figurenot yet calibrated
Small cubes are stacked in a corner as shown. Some are hidden from view. How many small cubes are there altogether?
CNT-14Counting cubes in a stack, including hidden onesalso GEO-13
KA-0012
5 points, difficulty 3 of 3Level 3–4not yet calibrated
How many two-digit numbers have digits that add up to 8?
CNT-04Caseworkalso CNT-01, NUM-02
KA-0018
5 points, difficulty 3 of 3Level 3–4not yet calibrated
A three-digit code uses only the digits 1, 2 and 3, and digits may repeat. How many such codes contain at least one 3?
CNT-09Complementary countingalso CNT-03, CNT-04
KA-0023
4 points, difficulty 2 of 3Level 5–6not yet calibrated
A password is one letter from A, B, C followed by two digits from 1 to 5. Digits may repeat. How many passwords are possible?
CNT-03The multiplication principlealso CNT-05
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-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-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-0040
5 points, difficulty 3 of 3Level 5–6not yet calibrated
A drawer holds 10 red socks, 10 blue socks and 10 green socks, all mixed up in the dark. How many socks must you take out to be sure of having a matching pair?
CNT-17The pigeonhole principlealso CNT-18, LOG-09
KA-0046
4 points, difficulty 2 of 3Level 3–4not yet calibrated
How many 2 by 2 squares fit on a 4 by 4 board, if they must line up with the grid?
CNT-12Counting by position (sliding window)also CNT-04
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

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