10让你爱上数学的游戏（10 make you love math games）.docVIP

10让你爱上数学的游戏（10 make you love math games） Digital black hole 6174 Pick a four-digit number (the number cant be the same), and all the Numbers from large to small, and all the Numbers from small to large, with the former minus the latter to get a new number. Repeat the above operation for the newly obtained number, and will inevitably get 6174 within 7 steps. For example, choose four digits 6767: 7766-6677 = 1089 9810-0189 = 9621 9621-1269 = 8352 8532-2358 = 6174 7641-1467 = 6174 ...... The black hole is called Kaprekar constant. For triple digits, theres also a digital black hole -- 495. 3x + 1 problem To start with any positive integer, repeat the following operation: if this number is even, divide it by 2; If this number is odd, then were going to expand it to 3 times and then add 1. Youll find that the sequence eventually becomes 4, 2, 1, 4, 2, 1... The loop. For example, the number chosen is 67, and according to the above rules can be obtained in turn: 67, 202, 101, 304, 152, 76, 38, 19, 58, 29, 88, 44, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1, 4, 2, 1,... Mathematicians tried a lot, and none escaped the 421 trap. But is it always going to be a 4, 2, 1 cycle for all the Numbers? The problem is a pit -- at first glance, the problem is very simple, the breach is a lot, and the mathematicians are jumping inside. Its easy to get out and get out, and many mathematicians have not solved the problem. There are countless mathematicians who have been recruited, which can be seen from the various aliases of the 3x + 1 problem: the problem of 3x + 1 is also known as Collatz conjecture, Syracuse problem, Kakutani problem, Hasse algorithm, Ulam problem and so on. Later, because the naming dispute is too big, simply let no one to shine, it is called 3x + 1. Until now, mathematicians have not proved that this rule is true for all Numbers. The speed of a special double digit multiplication If you have the same tens place in the two double digits, the single digi