MathDB

Celia chooses a number

n

and writes the list of natural numbers from

1

n

1, 2, 3, 4, ..., n-1, n.

At each step, it changes the list: it copies the first number to the end and deletes the first two. After

n-1

steps a single number will be written. For example, for

n=6

the five steps are:

1,2,3,4,5,6 \to 3,4,5,6,1 \to 5,6,1,3 \to 1,3,5 \to 5,1 \to 5

and the number

5

is written. Celia chose a number

n

between

1000

and

3000

and after

n-1

steps the number

1

was written. Determine all the values of

n

that Celia could have chosen. Justify why those values work, and the others do not.

Problem Statement