Whatcom County Math Championship – 2018 Potpourri – 4th Grade

1. How many corners are on a cube?

2. How many three-fourths are there in thirty-four and a half?

3. The Fibonacci numbers are those that start 1, 1, 2, 3, 5, 8... How many three-digit Fibonacci numbers are there?

A

4. B C How many ways can you transform this triangle so that the triangle is in the same position but the letters are in different places?

5. A, B, C, and D are increasing consecutive numbers less than 100. A is a square number, B is not prime, C is a cube number. What is D?

6. Rose has Q quarters and D dimes, with a total of $2.45, where Q and D are both counting numbers. How many different values of Q can Rose have?

7. The number 3 can be written as a sum of smaller positive integers in 3 ways: 1 + 1 + 1, 1 + 2, and 2 + 1. How many ways can 5 be written in this way?

8. How many even 2-digit numbers have an odd number as the sum of the digits?

9. What fraction of the area of the big triangle is the shaded triangle? Each angle marked with * is 30°.

*

* *

10. How many different routes are there from point A to point D which do not go through either points B and C more than once?

A B C D

Whatcom County Math Championship – 2018 Potpourri – 5th Grade

A

1. B C How many ways can you transform this triangle so that the triangle is in the same position but the letters are in different places?

2. A, B, C, and D are increasing consecutive numbers less than 100. A is a square number, B is not prime, C is a cube number. What is D?

3. Rose has Q quarters and D dimes, with a total of $2.45, where Q and D are both counting numbers. How many different values of Q can Rose have?

4. The number 3 can be written as a sum of smaller positive integers in 3 ways: 1 + 1 + 1, 1 + 2, and 2 + 1. How many ways can 5 be written in this way?

5. How many even 2-digit numbers have an odd number as the sum of the digits?

6. What fraction of the area of the big triangle is the shaded triangle? Each angle marked with * is 30°.

*

* *

7. How many different routes are there from point A to point D which do not go through either points B and C more than once?

A B C D

8. How many positive integers are divisors of 300?

9. A kitchen floor is to be tiled in the following way:!!

If the kitchen measures 23 tiles by 17 tiles, how many white tiles will be needed?

10. A number is semiprime if it is the product of exactly two prime factors: for example, 6 = 2 * 3 is semiprime, as is 25 = 5 * 5, but neither 5 nor 12 are. What is the largest two-digit semiprime number?

Whatcom County Math Championship – 2018 Potpourri – 6th Grade

1. The number 3 can be written as a sum of smaller positive integers in 3 ways: 1 + 1 + 1, 1 + 2, and 2 + 1. How many ways can 5 be written in this way?

2. How many even 2-digit numbers have an odd number as the sum of the digits?

3. What fraction of the area of the big triangle is the shaded triangle? Each angle marked with * is 30°.

*

* *

4. How many different routes are there from point A to point D which do not go through either points B and C more than once?

A B C D

5. How many positive integers are divisors of 300?

6. A kitchen floor is to be tiled in the following way:!!

If the kitchen measures 23 tiles by 17 tiles, how many white tiles will be needed?

7. A number is semiprime if it is the product of exactly two prime factors: for example, 6 = 2 * 3 is semiprime, as is 25 = 5 * 5, but neither 5 nor 12 are. What is the largest two-digit semiprime number?

8. How many ways can you transform this square so that the square is in the same position but the letters are in different places? A B

D C

9. A palindrome number is the same forwards and backwards, like 383 or 777. What is the sum of all 3-digit palindromes?

10. A, B, C, D, E, F, G and H are increasing consecutive numbers less than 100. A through G are not prime numbers, but H is. What is H? Whatcom County Math Championship – 2018 Potpourri – 7th + 8th Grade

1. How many different routes are there from point A to point D which do not go through either points B and C more than once?

A B C D

2. How many positive integers are divisors of 300?

3. A kitchen floor is to be tiled in the following way:!!

If the kitchen measures 23 tiles by 17 tiles, how many white tiles will be needed?

4. A number is semiprime if it is the product of exactly two prime factors: for example, 6 = 2 * 3 is semiprime, as is 25 = 5 * 5, but neither 5 nor 12 are. What is the largest two-digit semiprime number?

5. How many ways can you transform this square so that the square is in the same position but the letters are in different places? A B

D C

6. A palindrome number is the same forwards and backwards, like 383 or 777. What is the sum of all 3-digit palindromes?

7. A, B, C, D, E, F, G and H are increasing consecutive numbers less than 100. A through G are not prime numbers, but H is. What is H?

8. The number 486 has a digit sum of 18. How many positive numbers less than 1000 have a digit sum of 18?

9. The number 3 can be written as a sum of smaller positive integers in 3 ways: 1 + 1 + 1, 1 + 2, and 2 + 1. How many ways can 6 be written in this way?

10. In the figure below, each arc is formed by a circle centered on the dots shown. If the radius of the semicircle is 6, what is the shaded area? Round your answer to the nearest tenth.

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