There is a problem in Sun Tzu's Art of War, an important mathematical work in ancient China: "There are unknowns today, three and three numbers leave two, five and five numbers leave three, and seven and seven numbers leave two. What is the geometry of things? " Answer: "Twenty-three." This passage is translated into vernacular: "A lot of things, if you count three, there are two left; if you count five, there are three left; if you count seven, there are two left." How much is this pile? The answer is 23. "The solution to this problem is called the Sun Tzu Theorem, and it is called the Chinese remainder theorem abroad.

The solution to this problem is a poem by Cheng Dawei in the Ming Dynasty: "Three people are over seventy, five trees are twenty-one, and seven children are reunited for half a month. 105 later. " There are four numbers in this poem: 70,21,15, 105. As long as you keep these four figures in mind, this problem will be solved easily. Sun Tzu introduced this wonderful algorithm in detail in his calculation: every three numbers, the last remaining 1, take 1 70, the last remaining 2, take two 70; If the last remainder in every five is 1, take 1 2 1, and if the remainder is 2, take 221; Every seven numbers, if the final remainder is 1, take 1, and take two 15 for the remainder. Add up these numbers, and if the number is greater than 105, subtract 105, and these two sets of numbers are the smallest one and the second smallest one among many answers. For example, the above question is to take two 70s, three 2 1 and two 15. Since 2× 70+3× 21+2×15 = 233, it is greater than 105. If we subtract 105, we get 23. Surprisingly, this problem was solved in only a few steps.