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The whole Atlas

Number & Arithmetic15
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Patterns & Sequences7
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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-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-0069
4 points, difficulty 2 of 3Level 5–6not yet calibrated
In a class of 30, 18 play football and 14 play chess. 6 play both. How many play neither?
CNT-10Inclusion–exclusion with two setsalso CNT-09
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-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-0073
4 points, difficulty 2 of 3Level 5–6not yet calibrated
How many different four-letter arrangements can be made from the letters of the word MATH, using each letter once?
CNT-05Arrangements of a few objectsalso CNT-03
KA-0074
4 points, difficulty 2 of 3Level 5–6not yet calibrated
Two students are chosen from a group of six to represent the class. How many different pairs are possible?
CNT-06Selections of a few objectsalso CNT-08
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-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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