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Number & Arithmetic15
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Logic & Deduction11
Patterns & Sequences7
Modeling & Word Problems10
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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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Newest

177 problems

KA-0061
3 points, difficulty 1 of 3Level 3–4not yet calibrated
Each shape stands for a whole number. A triangle plus a triangle plus a triangle is 12, and a triangle plus a square is 9. What is the square?
NUM-14Operation puzzles and cryptarithmsalso LOG-08
KA-0062
4 points, difficulty 2 of 3Level 5–6not yet calibrated
24 pencils and 36 erasers are shared into identical gift bags, using every item. What is the largest number of bags possible?
NUM-05Factors, multiples, LCM and GCD by listingalso NUM-04
KA-0063
4 points, difficulty 2 of 3Level 3–4not yet calibrated
Which of these numbers can be divided exactly by both 4 and 9?
NUM-04Divisibility rules: 2, 3, 4, 5, 9, 10also NUM-01
KA-0064
3 points, difficulty 1 of 3Level 5–6not yet calibrated
Three quarters of a class of 28 travelled by bus. How many did not travel by bus?
NUM-09Fractions of a quantityalso CNT-09
KA-0065
4 points, difficulty 2 of 3Level 5–6not yet calibrated
A price goes up by 20%, then down by 20%. Compared with the original price, the final price is:
NUM-10Percentages and simple discountsalso NUM-09
KA-0066
4 points, difficulty 2 of 3Level 5–6not yet calibrated
The mean of four numbers is 9. Three of them are 5, 8 and 12. What is the fourth?
NUM-15Means, and working backwards from a meanalso LOG-08
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

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Showing 61–72 of 177