MathDB

(272) 6

Part of 1990 Tournament Of Towns

Problems(1)

TOT 272 1990 Autumn A J6 n different cards

Source:

6/8/2024
A deck consists of nn different cards. A move consists of taking out a group of cards in sequence from some place in the deck, and putting it back someplace else without changing the order within the group or turning any cards over. We are required to reverse the order of cards in the deck by such moves.
(a) Prove that for n=9n = 9, this can be done in 55 moves.
(b) Prove that for n=52n = 52, this i. can be done in 2727 moves, ii. can’t be done in 1717 moves, iii. can’t be done in 2626 moves. (SM Voronin, Tchelyabinsk)
combinatorics