John counts up from 1 to 13, and then immediately counts down again to 1, and then back up to 13, and so on, alternately counting up and down: What is the 1000th integer in his list?
I got 9
This might be a bit cheaty but i made a program do it
https://onlinegdb.com/_Xa6EYxOCj
Let's see if we can find a pattern ......
1 2 3 4 5 6 7 8 9 10
11 12 13 12 11 10 9 8 7 6
5 4 3 2 1 2 3 4 5 6
7 8 9 10 11 12 13 12 11 10
9 8 7 6 5 4 3 2 1 2
3 4 5 6 7 8 9 10 11 12
13 12 11 10 9 8 7 6 5 4
3 2 1 2 3 4 5 6 7 8
9 10 11 12 13 12 11 10 9 8
7 6 5 4 3 2 1 2 3 4
5 6 7 8 9 10 11 12 13 11
10 9 8 7 6 5 4 3 2 1
2 3 4 5 6 7 8 9 10 11
12 13 12 11 10 9 8 7 6 5
4 3 2 1 2 3 4 5 6 7
8 9 10 11 12 13 12 11 10 9
8 7 6 5 4 3 2 1 2 3
4 5 6 7 8 9 10 11 12 13
12 11 10 9 8 7 6 5 4 3
2 1 2 3 4 5 6 7 8 9
10 11 12 13 12 11 10 9 8 7
6 5 4 3 2 1 2 3 4 5
6 7 8 9 10 11 12 13 12 11
10 9 8 7 6 5 4 3 2 1
The pattern repeats after every 120 digit
1000 mod 120 = 40
The 1000th digit is 9