In (a variant of) the game fizz buzz, the positive integers are considered in order starting from 1 but replacing any number which is a multiple of 3 with ‘fizz’ and replacing any number which is a multiple of 5 with ‘buzz’. When ‘fizz’ or ‘buzz’ arise they are called out. So the game begins:
1, 2, fizz, 4, buzz, fizz, 7, 8, fizz, buzz, 11, fizz, 13, 14, fizz buzz, 16,….
Given ‘fizz buzz’ counts as two numbers being called out, what is the 2012th number to be said aloud?
Reveal Solution
From 1 to 15 (and from 15n +1 to 15(n+1) for any n ) exactly 8 numbers will be said aloud. 2012 = 8 x 251 + 4 so by the time the game reaches 15 x 251 = 3765 then 8 x 251 = 2008 numbers will have been said aloud. The fourth number to be said aloud after this will be 3772.
