IMSO

[nowhere]

1. A deck consists of n different cards. A move consists of taking out a stack of consecutive cards from the deck, and then putting the same stack back somewhere else within the deck without flipping any of the cards or changing the other of cards within the stack. You are required to reverse the original order of cards in the deck by such moves. What is the minimum number of moves required if
1.1 n = 5
1.2 n = 9
1.3 n = 13

2. In a chess tournament with 15 players. every two play a game against each other once. A win is worth 2 points, a draw 1 point and a loss 0 points. A prize is given to any player with a total score of at least 20 points. What is the maximum number of prize winners?

3. A set of dominoes consists of the following 28 pieces:

The basic rule in playing dominoes is that, when two dominoes share a common edge, the numbers of dots inside the two squares which share that edge must be the same. The figure shows an example of a hollow square formed from all 28 domino pieces in accordance with basic rule. The total number of dots along the lower side is 74, the total along the right side is 47 points and the total along each of the other two sides is 59. The difference between the largest and the smallest totals is 74 - 47 = 27. Rearrange the domino pieces so that the difference between the largest and the smallest totals is as small as possible.