Throwing Number

Consider the sequence of positive integers \(1,2,3,4,5,6, \ldots \). An operation throw consists of taking the first number \(k\) and move it to the back of the \((k+1)^\text{th}\) number. For example,

1
2
3
4
5
6
seq 1 : 1 2 3 4 5
seq 2 : 2 1 3 4 5
seq 3 : 1 3 2 4 5 
seq 4 : 3 1 2 4 5 
seq 5 : 1 2 4 3 5
seq 6 : 2 1 4 3 5

Let \(S\) be the first sequence that has number 1000 as its leading number. What is the last 3 digit of \(S\)?

Bonus: How about the second sequence that has number 1000 as its leading number?

×

Problem Loading...

Note Loading...

Set Loading...