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The whole Atlas

Number & Arithmetic15
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Patterns & Sequences7
Modeling & Word Problems10
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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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19 problemsClear all filters

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-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-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-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-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-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

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