Question 1

Which of the following numbers is found in both the Fibonacci sequence and the set of perfect squares, but is NOT a power of 2, for numbers less than 50?

Accepted Answer

1

Question 2

According to the rules of the game, which player is most likely to run out of numbers first, given their favorite numbers less than 50?

Accepted Answer

Fibonacci (Fibonacci numbers)

Question 3

If the Venn diagram has three circles labeled F (Fibonacci), P (Powers of 2), and S (Squares), which region is empty at the end of the game?

Accepted Answer

The region shared by all three sets (F ∩ P ∩ S)

Question 4

Which player has the most exclusive numbers (numbers not shared with any other set) at the end of the game?

Accepted Answer

Sommerville (perfect squares)

Question 5

Which of the following numbers is both a power of 2 and a perfect square, but NOT a Fibonacci number, for numbers less than 50?

Accepted Answer

16

Question 6

If the players place their lowest available number in the Venn diagram each turn, which number is placed first?

Accepted Answer

1

Question 7

How many numbers less than 50 are both Fibonacci numbers and powers of 2?

Accepted Answer

1

Question 8

Which of the following numbers is found in all three sets: Fibonacci numbers, powers of 2, and perfect squares, for numbers less than 50?

Accepted Answer

There is no such number

Question 9

If the players continue until all their favorite numbers less than 50 are placed, how many numbers are placed in total?

Accepted Answer

29

Question 10

Suppose the players are asked to find the sum of all numbers that are both perfect squares and Fibonacci numbers less than 50. What is the sum?

Accepted Answer

$$1 + 4 + 9 = 14$$

Question 11

If Pascal's favorite numbers are all powers of 2 less than 50, how many such numbers are there?

Accepted Answer

6

Question 12

Which of the following is NOT a perfect square less than 50?

Accepted Answer

48

Question 13

If Fibonacci's favorite numbers are all Fibonacci numbers less than 50, what is the highest such number?

Accepted Answer

34

Question 14

Which of the following numbers is both a perfect square and a power of 2, for numbers less than 50?

Accepted Answer

16

Question 15

If Sommerville's favorite numbers are all perfect squares less than 50, how many such numbers are there?

Accepted Answer

7

Question 16

If the players are asked to find the intersection of Pascal's and Sommerville's favorite numbers, which numbers are included?

Accepted Answer

1, 4, 16

Question 17

Which of the following numbers is a Fibonacci number but NOT a perfect square or a power of 2, for numbers less than 50?

Accepted Answer

21

Question 18

If the players are asked to find the union of all their favorite numbers less than 50, how many unique numbers are there?

Accepted Answer

18

Question 19

If the players are asked to find the number of numbers that are only in Pascal's set (powers of 2) and not in the other sets, how many such numbers are there?

Accepted Answer

3

Question 20

If the players are asked to find the number of numbers that are only in Sommerville's set (perfect squares) and not in the other sets, how many such numbers are there?

Accepted Answer

4

Venn Diagram Reasoning with Number Sets (Fibonacci, Powers of 2, and Squares)

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