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

By counting the combinations, we will see that there are 10 combinations such that the sum gives a Fibonacci number.

How to count the combinations?

We have two number cubes with 6 outcomes each, such that we have a total of 36 combined outcomes.

For each dice, the outcomes are:

{1, 2, 3, 5, 8, 13}

Now, let's count the combinations that also give a Fibonacci number (these are given by adding two consecutive numbers in the sequence).

I will list each possible red outcome, then the blue outcomes that would give a Fibonacci term, and then we can count the number of combinations.

• Red         Blue           number of combinations.
• 1                2                             1
• 2              1, 2                           2
• 3              2, 3                          2
• 5             3, 8                           2
• 8             5, 13                          2
• 13            8                               1

Adding the numbers of combinations, we have:

C = 1 + 2 + 2 + 2 + 2 + 1 = 10

There are 10 combinations that give a Fubbonaci number.

If you want to learn more about combinations, you can read:

brainly.com/question/2280026