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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 1000th integer in her list?

 May 28, 2020
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When Suelyn counts from 1-2-3-4-5-6-7-8-9-8-7-6-5-4-3-2     (16 numbers)

                                           1-2-3-4-5-6-7-8-9-8-7-6-5-4-3-2     (anothe 16 numbers)

                                           etc.

In cycles of 16.

 

Divide 1000 by 16 and you get 62 with a remainder of 8.

So, there are 16 cycles, plus a remaining 8 numbers.

The 1000th number will be the eighth number on the list  =  8.

 May 28, 2020

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