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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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13 problemsClear all filters

KA-0003
4 points, difficulty 2 of 3Level 3–4has a figurenot yet calibrated
A large triangle is cut by two lines from its top corner into three small triangles side by side. How many triangles of any size appear in the picture?
CNT-13Counting shapes hidden inside a figurealso CNT-04
KA-0009
4 points, difficulty 2 of 3Level 3–4has a figurenot yet calibrated
Small cubes are stacked in a corner as shown. Some are hidden from view. How many small cubes are there altogether?
CNT-14Counting cubes in a stack, including hidden onesalso GEO-13
KA-0023
4 points, difficulty 2 of 3Level 5–6not yet calibrated
A password is one letter from A, B, C followed by two digits from 1 to 5. Digits may repeat. How many passwords are possible?
CNT-03The multiplication principlealso CNT-05
KA-0046
4 points, difficulty 2 of 3Level 3–4not yet calibrated
How many 2 by 2 squares fit on a 4 by 4 board, if they must line up with the grid?
CNT-12Counting by position (sliding window)also CNT-04
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-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-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-0154
4 points, difficulty 2 of 3Level 7–8not yet calibrated
In a class of 30 students, 18 play football and 15 play chess. Exactly 7 students do both. How many students play neither?
CNT-10Inclusion–exclusion with two setsalso CNT-09, CFT-01
KA-0163
4 points, difficulty 2 of 3Level 9–10not yet calibrated
A club has 8 members. In how many ways can a group of 3 be chosen to attend a conference, if the three places are all the same?
CNT-06Selections of a few objectsalso CNT-16, CFT-01
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

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