World Mathematics Invitational 2024 Problem Booklet B (Grade 4)

Compute 2 + 12 + 22 + 32 + 1992 + 2002 + 2012 + 2022.

• 8088

• 8084

• 8086

• 8094

• 8096

3-digit numbers □20 is divisible by 24. Find the sum of all the possible values of □’s.

• 7

• 13

• 5

• 8

• 9

How many triangles are there in the figure? Don’t miss the big triangles.

• 128

• 127

• 125

• 124

• 120

Start from 1, Daniel writes a sequence of successive natural numbers 123456789101112⋯⋯. If he stops after he writes a certain natural number and finds that he writes a total of twenty-four 1’s, how many 2’s does he write?

• 19

• 20

• 21

• 22

• 23

A 4-digit password is formed by digits 1, 2, and 3. If 1 can be used 1 time at most, 2 can be used 2 times at most, and 3 can be used 3 times at most, how many different possibilities are there for this password?

• 36

• 24

• 38

• 40

• 42

Fill 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 in the ten circles respectively where each number can only be used once. If the sum of the numbers at the three vertices of each shaded triangle is 16, find the sum of the digits of the product of the numbers at the three vertices of the large triangle.

• 7

• 9

• 10

• 4

• 5