Escape The Even Demon

Number Theory Level 3

You are the village chief. Your village has 1000 residents including yourself. One day the ferocious EVEN DEMON attacks your village and snarls,

"All you 1000 villagers stand in a large CIRCLE, numbering yourself from 1 to 1000. Starting from number 1, I will eat every second villager (which means he will eat villager number 2, then villager number 4 and so on) and keep going around and around the circle eating up every second villager and keep doing this till there is only 1 villager left. That last villager I will spare and he is free to escape."

Since you are the village chief, you have the right to choose where you wish to stand.

In the original circle of 1000 villagers which number will you choose to stand at to be the last villager standing and escape the clutches of the EVEN DEMON?

This problem is not an original. It is adapted from a famous problem recorded by a Jewish historian.


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