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The whole Atlas

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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14 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-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-0051
3 points, difficulty 1 of 3Level 3–4not yet calibrated
How many of the numbers from 1 to 20 are not multiples of 3?
CNT-09Complementary countingalso CNT-01
KA-0054
3 points, difficulty 1 of 3Level 3–4has a figurenot yet calibrated
A rectangle is divided by two vertical lines into three parts. How many rectangles of any size are in the picture?
CNT-13Counting shapes hidden inside a figurealso CNT-01
KA-0067
3 points, difficulty 1 of 3Level 3–4has a figurenot yet calibrated
A cafe offers 3 main courses and 2 puddings. How many different two-course meals can be ordered?
CNT-02Tree diagramsalso CNT-03
KA-0068
4 points, difficulty 2 of 3Level 3–4not yet calibrated
A coin is tossed three times. In how many of the possible outcomes are there exactly two heads?
CNT-02Tree diagramsalso CNT-01, CNT-04
KA-0072
3 points, difficulty 1 of 3Level 3–4not yet calibrated
How many different two-digit numbers can be written using only the digits 1, 2 and 3, if a digit may be used twice?
CNT-01Systematic listingalso CNT-03
KA-0076
4 points, difficulty 2 of 3Level 3–4not yet calibrated
In how many ways can 7 be written as the sum of two different whole numbers bigger than zero? Swapping the order does not make a new way.
CNT-04Caseworkalso CNT-01, NUM-03

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