What interesting mathematical knowledge is contained in playing cards?

Poker is a popular entertainment tool. According to legend, as early as the battle between Chu and Han at the end of Qin Dynasty, General Han Xin invented a card game to relieve soldiers' homesickness. Because these cards are only the size of leaves, they are called "Ye Zi Xi" and later developed into 54 playing cards.

The 54 patterns of playing cards are also wonderful to explain:

The king represents the sun, Xiao Wang represents the moon, and the remaining 52 cards represent 52 weeks in a year;

Heart-shaped, diamond, plum blossom and spades symbolize spring, summer, autumn and winter respectively.

There are 13 cards in each suit, which means there are 13 weeks in each season.

If J, Q and K are regarded as 1 1, 12, 13 points, then the king and Xiao Wang are half points, and the total number of points in a deck of playing cards is exactly 365 points. In leap years, Wang and Wang calculate 1 point and ***366 points respectively.

Experts generally believe that the above explanation is not a coincidence, because the design and invention of playing cards are inextricably linked with astrology, divination, astronomy and calendar. But playing cards has a lot of mathematical knowledge, you know?

1. Symmetric graphics in playing cards

There are four colors in playing cards: hearts, diamonds, clubs and spades. Each color is an axisymmetric figure, and the diamonds are not only axisymmetric figures, but also centrally symmetric figures. It is precisely because of these symmetrical characteristics that they have wonderful math problems.

For example, in 2007, in seven cities including Baiyin, Gansu Province, the fourth item of the new curriculum mathematics test:

Put four playing cards on the table, as shown in the figure (1). Xiao Min rotates one of the cards 180 to get the card as shown in Figure (2), so the card she rotates is () from the left.

A. the first b, the second c, the third d and the fourth

This problem is novel in design and ingenious in conception. Through the operation of playing cards, this paper explores the changing rules in graphics, so that students can experience the occurrence, development and application of knowledge. Students will find that the two graphs (1)(2) have not changed, but the clever setting of the problem is that only by rotating the square 9 can two graphs (1)(2) appear. The test questions effectively examine students' understanding and mastery of the knowledge point of central symmetry, and also cultivate students' ability to find and solve problems.

Second, the calculation problems in playing cards

There is a kind of "2 1 point" game, and the rules of the game are as follows: four cards (excluding big and small kings) are randomly selected from a deck of playing cards, in which A, 2, 3, …, and K represent 1, 2, 3, …, 13 in turn, and the numbers on the cards are added, subtracted, multiplied and divided.

For example, four cards (excluding the king and the king) are randomly selected from a deck of playing cards, where a, 2, 3, …, and k represent 1, 2, 3, …, 13 in turn, red playing cards, spades and diamonds represent positive numbers, and grass flowers represent negative numbers. The four cards Xiao Cong drew were hearts 3 and spades. The essence of this game is to use the above rules to write three different formulas for four rational numbers 3, 4, 10 and -6, so the result is 24. For example,10-4-3× (-6) = 24; 4-(-6)÷3× 10; Can you write another one?

Through the calculation of "twenty-four points" in playing cards, we can cultivate students' interest in learning rational number operation, make boring rational number operation glow with vitality in a happy state, and at the same time let students increase their knowledge in the game, let students' thinking ability diverge, so as to further sublimate their computing ability. This kind of test not only makes the calculation teaching develop and improve harmoniously in arithmetic, algorithm and skills, but also embodies the standards of the new curriculum, and really advocates the rational calculation teaching which is solid and effective and respects the development of students' personality.

Third, the orderly arrangement in playing cards.

Each new deck of playing cards is arranged in a certain order, that is, the first card is Wang, the second is Xiao Wang, and then there are four suits of spades, hearts, diamonds and clubs. The cards of each suit are arranged in the order of A, 2, 3, …, J, Q and K. If such playing cards are played according to certain rules, a good proposition can be obtained.

For example, item 8 of the 2005 national junior high school mathematics competition:

There are two decks of playing cards. The order of each deck is: the first deck is king, the second deck is Xiao Wang, and then the arrangement of spades, hearts, diamonds and clubs. The cards of each suit are arranged in the order of A, 2, 3, …, J, Q and K. Someone stacks two decks of playing cards arranged as above, then throws the first card from top to bottom, the second card at the bottom, the third card at the bottom and the fourth card at the bottom ... and so on until there is only one card left, and the remaining cards are _ _ _ _ _ _ _ _. I just finished reading the test questions, and I feel that I can't start. However, we can start with two simple playing cards, and according to the rules, we can find that the rest is the second card. If it is four playing cards, according to the rules, you can find that the rest is the second card; If it is eight playing cards, according to the rules, you can find that the rest is the eighth card; Then we will find that the number of playing cards is 2, 22, 23, …, 2n. According to the above method, the remaining cards are the last of these cards. For example, there are only 64 cards in hand. According to the above operation method, only the 64th card is left. At present, there are 108 in hand, which is more than 108-64=44 (sheets). If you follow the above operation method, you will lose 44 cards first, and at this time you just have 64 cards in your hand, and the 88th card in the original order is just at the bottom of your hand. And 88-54-2-26=6, according to the design order of the two decks, the last card left is the square 6 in the second deck. Wonderful ideas form wonderful test questions. This test makes good use of the orderly arrangement of playing cards, permeates the general and special mathematical ideas, and enables students to fully develop their creative thinking in their interest in playing cards.

Poker is an ancient and very popular game tool. The randomness of different card combinations is not only challenging, but also contains many interesting mathematical problems. Playing poker can stimulate students' interest in mathematics and cultivate their logical thinking ability and reasoning ability.