Required Mathematical Intelligence

Chapter 77 Ace
In a game of poker, someone has a deck of cards like this:

(1) There are exactly thirteen cards.

(2) At least one card of each suit.

(3) The number of sheets of each suit is different.

(4) There are five hearts and squares in total.

(5) There are six hearts and spades in total.

(6) There are two cards belonging to the suit of the "trump card".Among the four suits of hearts, spades, diamonds and clubs, which one is the "trump" suit?
[Answer: According to (1), (2), and (3), the distribution of the four suits in this person's hand is one of the following three possible situations:

(a) 1237
(b) 1246
(c) 1345
According to (6), case (c) is ruled out because none of the suits in it are two cards.According to (5), case (a) is ruled out because the sum of cards of any two suits in it is not six.

Therefore, (b) is the actual suit distribution.According to (5), there are either two hearts and four spades, or four hearts and two spades.

According to (4), there are either one heart and four diamonds, or four hearts and one diamond.Combining (4) and (5), there must be four hearts; thus there must be two spades.Therefore, spades are the trump suit.

To sum up, this person has four hearts, two spades, one diamond and six clubs in his hand. ]
(End of this chapter)