Question 114
A prestidigitator and his assistant have a deck of cards; back sides of all the cards look identical, the front side of each card is painted in one of $2017$ colors (there are $1000000$ cards of each color in the deck). They want to perform the following trick. The prestidigitator goes out of the room. The spectators put $n$ cards facing front in a row onto the table. The assistant looks at them and turns all the cards except one facing back side (he does not change the order of the cards). Finally, the prestidigitator comes in, stares at the table, and guesses the color of one of the cards facing back. Find the least value of $n$ for which the prestidigitator and the assistant can agree on their actions in advance so that they will do the trick for sure.
(I. Bogdanov, K. Knop)
(I. Bogdanov, K. Knop)