MathDB

10

Part of 2011 QEDMO 10th

Problems(1)

n coins trick, a magician and his assistant

Source: 10th QEDMO p10 Seniors (8-10. 12. 2011) https://artofproblemsolving.com/community/c1512515_qedmo_200507

5/16/2021
The great Zagier and his assistant performed a magic trick, which was a natural one number nn involved. To do this, Zagier distributes nn 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 kk from 11 to nn. 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 kk to the public. For which natural numbers nn 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?
combinatorics