jmc

Question

Suelyn counts up from 1 to 9, and then immediately counts down again to 1, and then back up to 9, and so on, alternately counting up and down (1, 2, 3,4,5,6,7,8,9,8,7,6,5,4,3,2,1,2,3,4, ). What is the 1000^th integer in her list?

Accepted Answer

We can treat this list as a sequence with a repetitive pattern. We see the sequence repeats itself every 16 elements (from 1 to 9 then back to 2). Because 1000 divided by 16 is 62 with a remainder of 8, to get 1000 terms in this list, we repeat the block 62 times, and then go 8 more elements. This means that the 1000^th integer is the same as the 8^th integer, which is 8.