Question

The Fibonacci sequence 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, … is formed by summing two consecutive numbers to get the next number. The number after 55 is 34 + 55 = 89. A Fibonacci game cube has a different Fibonacci number on each face selected from the set {1, 2, 3, 5, 8, 13}. One red and one blue Fibonacci game cube are tossed together. How many of the 36 possible outcomes show a pair of numbers on the tops of the cubes whose sum is also a Fibonacci number?

Answer 1

Answer: 11

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Step-by-step explanation:

The possible Fibonacci sums are:

• 1+1 = 2
• 1+2 = 3
• 2+3 = 5
• 3+5 = 8
• 5+8 = 13
• 8+13 = 21

Look at the chart below and highlight when those sums occur.

I've highlighted them in green. A fairly interesting pattern forms. There are two instances of each sum in the set {3,5,8,13,21}. That set has 5 items. The sum "2" only shows up once.

So we have 2*5+1 = 11 Fibonacci sums overall.