MathDB

The great Zagier and his assistant performed a magic trick, which was a natural one number

n

involved. To do this, Zagier distributes

n

identical coins (with heads and tails on the sides) and then leave the hall. The audience now arranges the coins in a row, you can choose the top side of each coin as you like, and then tell the assistant one natural number

k

from

1

n

. This then turns over exactly one coin, whereupon Zagier is brought in and placed in front of said coins. To the surprise of the non-mathematical, he can name the number

k

to the public. For which natural numbers

n

can this trick be carried out, if the two are allowed to coordinate only before the show, but during the show they do not use any magic tricks?

Problem Statement