Multiple choice general knowledge math & puzzles

Boxes numbered 1, 2, 3, 4, and 5 are kept in a row, and they are to be filled with either a red or a blue ball, such that no two adjacent boxes can be filled with blue balls. How many different arrangements are possible, given that all balls of a given colour are exactly identical in all respects?

  1. 8

  2. 10

  3. 15

  4. 22

  5. 13
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

This is a duplicate of question 5425 with the same content but different options. Using the combinatorial formula for placing k blue balls in 5 boxes with no two adjacent: arrangements = C(5-k+1, k). For k=0: C(6,0)=1; k=1: C(5,1)=5; k=2: C(4,2)=6; k=3: C(3,3)=1. Total = 1+5+6+1 = 13. Option E (13) is correct.

AI explanation

Each of the 5 boxes is red or blue with no two adjacent boxes both blue. This equals the number of length-5 binary strings with no two adjacent 1s (blue), which is the Fibonacci number F(7) = 13. Check: length 1 = 2, length 2 = 3, length 3 = 5, length 4 = 8, length 5 = 13. So 13 arrangements are possible. The original key (22) was incorrect and 13 was missing from the options; 13 has been added as the correct answer.

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