Skip to main content

Atlas
Problems
Diagnostic
Mock
Papers
About

The whole Atlas

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

Loading…

About
Sign in
Worksheets
Privacy
Terms
License
Contact
GitHub

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

Independent project. Not affiliated with or endorsed by Math Kangaroo in USA, NFP.

Home
Atlas
Problems
Papers

Browse the problems

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

Sort

Id
Hardest first
Newest

10 problemsClear all filters

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

Browse the problems — Kangaroo Atlas