Escape Satan And Save Mathematics!

This problem was inspired by this problem.

After having his demon henchmen thwarted by the cunning mathematician village chiefs of Earth,the devil himself comes down to Earth to get rid of the problem once and for all.

Confidently he snarls

" All you people of Earth stand in a large CIRCLE and number yourself starting from \(1\) to \(10^7\). I will devour every \(666th\) person and keep going around and around the circle eating up every \(666th\) person and keep doing this till there is only \(1\) person left. That last person I will spare and he is free to escape. "

You are the last living descendant of the mathematician village chiefs and need to ensure that you survive so that mathematics will not perish from Earth.

Which number will you choose to be the last person standing and escape the clutches of Satan?

Details and assumptions

  • Assume all this happened a long time ago and that Earth only had \(10^7\) inhabitants.
  • Satan will start eating from the \(666\)th person.
  • This is an instance of a very famous problem called the Josephus Problem.


  • It there were \(9\) people and every \(5\)th person was eaten the people eaten would be \(5\rightarrow 1\rightarrow 7\rightarrow 4\rightarrow 3\rightarrow 6\rightarrow 9\rightarrow 2\) leaving the \(8\)th person alive.

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