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The whole Atlas

Number & Arithmetic15
Counting18
Geometry & Visualization18
Logic & Deduction11
Patterns & Sequences7
Modeling & Word Problems10
Contest Craft12

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Code is MIT. Problems, skills, and explanations are CC BY-NC-SA 4.0. Practice never requires an account and nothing here is paywalled.

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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-0169
3 points, difficulty 1 of 3Level 11–12not yet calibrated
What is the remainder when 7 to the power 100 is divided by 5?
NUM-06Remainders and modular cyclesalso NUM-07, PAT-03
KA-0170
3 points, difficulty 1 of 3Level 11–12not yet calibrated
What is the size of one interior angle of a regular twelve-sided polygon?
GEO-05Angles on lines, in triangles, in polygonsalso CFT-10, CFT-11
KA-0171
3 points, difficulty 1 of 3Level 11–12not yet calibrated
A sequence is defined by a(1) = 2 and a(n+1) = 2 a(n) - 1 for every n. What is a(6)?
PAT-05Recursive rulesalso CFT-03, PAT-07
KA-0172
4 points, difficulty 2 of 3Level 11–12not yet calibrated
A committee of 4 must be formed from 5 boys and 4 girls, and it must contain exactly 2 boys and 2 girls. How many different committees are possible?
CNT-06Selections of a few objectsalso CNT-04, CNT-16
KA-0173
4 points, difficulty 2 of 3Level 11–12not yet calibrated
Each of the four edges of a square is painted either black or white. Two paintings count as the same if one can be rotated onto the other. How many genuinely different paintings are there?
CNT-15Counting up to symmetryalso CNT-04, LOG-11
KA-0174
4 points, difficulty 2 of 3Level 11–12not yet calibrated
A driver travels from one town to another at an average of 60 km/h and returns along the same road at an average of 40 km/h. What is the average speed for the whole journey?
MOD-03Rate, time, distancealso MOD-08, CFT-11
KA-0175
5 points, difficulty 3 of 3Level 11–12not yet calibrated
What is the smallest number n such that ANY collection of n whole numbers must contain two of them whose difference is divisible by 7?
CNT-17The pigeonhole principlealso NUM-06, LOG-09
KA-0176
5 points, difficulty 3 of 3Level 11–12not yet calibrated
An 8 by 8 chessboard has two opposite corner squares removed, leaving 62 squares. Each domino covers exactly two squares that share an edge. Can the 62 squares be covered exactly by 31 dominoes?
LOG-07Coloring argumentsalso LOG-09, CNT-15
KA-0177
5 points, difficulty 3 of 3Level 11–12not yet calibrated
How many diagonals does a convex polygon with 12 sides have? A diagonal joins two vertices that are not already joined by a side.
CNT-16Overcount, then correctalso CNT-06, GEO-05

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