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The whole Atlas

Number & Arithmetic15
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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-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
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-0079
3 points, difficulty 1 of 3Level 3–4not yet calibrated
Which of these is true of every rectangle?
GEO-06Properties of triangles and quadrilateralsalso GEO-08
KA-0080
4 points, difficulty 2 of 3Level 5–6not yet calibrated
An isosceles triangle has an angle of 100 degrees. How big is each of the other two angles?
GEO-06Properties of triangles and quadrilateralsalso GEO-05
KA-0081
4 points, difficulty 2 of 3Level 3–4has a figurenot yet calibrated
A solid is built from unit cubes. The two pictures show it from above and from the front. What is the smallest number of cubes it could be made of?
GEO-12Views of a solid: top, front, sidealso GEO-13, CNT-14
KA-0082
5 points, difficulty 3 of 3Level 5–6has a figurenot yet calibrated
A room is 8 m long, 4 m wide and 2 m high. An ant walks across the floor and the walls from one bottom corner to the far top corner. What is the shortest distance in metres?
GEO-17Shortest paths on and around shapesalso GEO-10, GEO-01
KA-0083
3 points, difficulty 1 of 3Level 3–4not yet calibrated
A rectangle has a perimeter of 20 cm. One of its sides is 6 cm. What is its area in square centimetres?
GEO-01Perimeter and area of rectilinear shapes
KA-0084
4 points, difficulty 2 of 3Level 5–6not yet calibrated
A square of side 6 cm is cut along a midline into two identical rectangles. What is the perimeter of one of them?
GEO-03Area by dissection and rearrangementalso GEO-01

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