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

50 problemsClear all filters

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-0017
5 points, difficulty 3 of 3Level 3–4not yet calibrated
Ana says "Bo is lying." Bo says "Cal is lying." Cal says "Ana and Bo are both lying." How many of the three are telling the truth?
LOG-02Truth-tellers and liarsalso LOG-01, LOG-09
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-0020
5 points, difficulty 3 of 3Level 3–4has a figurenot yet calibrated
A square sheet is folded in half top to bottom, then in half left to right. One hole is punched through all the layers. How many holes are in the unfolded sheet?
GEO-15Paper folding and hole punchingalso GEO-08, GEO-09
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-0028
5 points, difficulty 3 of 3Level 5–6not yet calibrated
Seven cups all stand upside down. In one move you must turn over exactly two cups. Can all seven ever stand the right way up?
LOG-05Parity argumentsalso NUM-03, LOG-09
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-0034
5 points, difficulty 3 of 3Level 5–6has a figurenot yet calibrated
A 4 by 4 board has two opposite corner squares removed, leaving 14 squares. Each domino covers exactly two squares that share an edge. Can 7 dominoes cover the board?
LOG-07Coloring argumentsalso LOG-05, GEO-14
KA-0037
5 points, difficulty 3 of 3Level 5–6not yet calibrated
What is the units digit of 7 multiplied by itself 2026 times, that is 7 to the power 2026?
NUM-07Last-digit behavior of products and powersalso NUM-06, PAT-03
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-0043
5 points, difficulty 3 of 3Level 5–6not yet calibrated
A bag holds 5 black and 6 white stones. You repeatedly remove two stones: if they match you put a black one in, if they differ you put a white one in. What colour is the last stone?
LOG-06Invariants and monovariantsalso LOG-05, NUM-03
KA-0045
5 points, difficulty 3 of 3Level 5–6not yet calibrated
A number is 4 more than a third of itself. Which of the choices is that number?
CFT-04Back-solve from the answer choicesalso CFT-05, MOD-01

1
2
5

Showing 1–12 of 50

Browse the problems — Kangaroo Atlas