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

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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-0145
3 points, difficulty 1 of 3Level 5–6not yet calibrated
A counter sits at the point (3, 5) on a grid. It moves 4 squares right and 2 squares down. Where is it now?
GEO-02Grid coordinates and lattice reasoningalso GEO-09
KA-0146
3 points, difficulty 1 of 3Level 5–6not yet calibrated
Suppose it is true that some birds cannot fly. Which of these must also be true?
LOG-01Reading a logical statement preciselyalso LOG-09
KA-0147
4 points, difficulty 2 of 3Level 5–6not yet calibrated
Two circles touch on the outside. One has a radius of 3 cm and the other a radius of 5 cm. How many centimetres apart are their centres?
GEO-07Circles: radius, diameter, and touching circlesalso GEO-01
KA-0148
4 points, difficulty 2 of 3Level 5–6not yet calibrated
What is the smaller angle between the hands of a clock at exactly 4 o'clock?
GEO-18Clock geometry: hands, angles, timesalso GEO-05, NUM-11
KA-0149
4 points, difficulty 2 of 3Level 5–6not yet calibrated
What is the units digit of 3 multiplied by itself 100 times, that is 3 to the power 100?
NUM-07Last-digit behavior of products and powersalso NUM-06, PAT-03
KA-0150
4 points, difficulty 2 of 3Level 3–4not yet calibrated
A diagonal joins two corners of a shape that are not next to each other. How many diagonals does a hexagon have?
CFT-03Try small cases firstalso CNT-08, GEO-06
KA-0151
3 points, difficulty 1 of 3Level 7–8not yet calibrated
A bread recipe uses flour and sugar in the ratio 5 to 3. The two together weigh 320 grams. How much of that is flour?
NUM-11Ratio as parts of a wholealso CFT-01, CFT-10
KA-0152
3 points, difficulty 1 of 3Level 7–8not yet calibrated
In a triangle, one angle measures 30 degrees. Of the other two angles, one is exactly twice the other. What is the largest angle in the triangle?
GEO-05Angles on lines, in triangles, in polygonsalso MOD-01, CFT-02
KA-0153
3 points, difficulty 1 of 3Level 7–8not yet calibrated
A jacket costs 80 pounds. In January the price rises by 20 percent. In February the new price falls by 20 percent. What is the price at the end of February?
NUM-10Percentages and simple discountsalso CFT-11, CFT-10
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-0155
4 points, difficulty 2 of 3Level 7–8not yet calibrated
A photograph measures 8 cm by 12 cm. It is enlarged so that the shorter side becomes 20 cm, and the shape is not distorted. How long is the longer side of the enlargement?
GEO-16Scaling and similar figuresalso NUM-11, CFT-11
KA-0156
4 points, difficulty 2 of 3Level 7–8not yet calibrated
A pattern is built in rows. The first figure has 1 row, the second has 2 rows, and so on. In every figure, the first row has 1 dot, the second has 3 dots, the third has 5 dots, and each row after has 2 more dots than the one above it. How many dots are in the eighth figure?
PAT-04Growth patterns and figurate numbersalso CFT-03, PAT-02

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