[Guess a number] Tell A to the two numbers, and product to B to find out what these two numbers are.

The two numbers from 1 to 20 tell a, and the product tells B. A says that he does not know the number, and B also says that he does not know. Then a says that he knows, and B says that he also knows, what are the two numbers?

Analysis:

Set to S and product to M.

First, A: I don't know.

Note: s can be divided into multiple combinations, while 2 = 1 + 1, 3 = 1 + 2, 40 = 20 + 20, 39 = 19 + 20. There is only one decomposition method, therefore, s belongs to the [] set.

Second, B: I don't know either.

Note: m can also be divided into multiple combinations, so m is not a prime number.

Furthermore, A: Now I know.

Note:In the S decomposition method, only one of them is a combination after multiplication, and all other decomposition methods are a prime number after multiplication.. In this way, a can not know according to B, and the possibility that all multiplication is a prime number (M is a prime number, and there is only one Decomposition Method: 1 * prime number, after the remainder is multiplied, the combination of the numbers is the solution obtained by.

After multiplication, there is a prime number: only 1 * prime number = prime number!

All prime numbers from 1 to 20: t = {2, 3, 5, 7, 11, 13, 17, 19 }.

Set X to any prime number in T. Then, the possible values of S are: {2 + 1, 3 + 1, 5 + 1, 7 + 1, 11 + 1, 13 + 1, 17 + 1, 19 + 1}, I .e.: Ss = {3, 4, 6, 8, 12, 14, 18, 20}

S = 3: 3 is not in the [4, 38] Set, exclude;

S = 4: 4 = 2 + 2 = 1 + 3, () Multiply by 4 (non-prime number, meet the condition), () Multiply by 3 (prime number, excluded );

When S = 6: 6 = 1 + 5 = 2 + 4 = 3 + 3, multiply by 5, 8, 9, and there are two composite numbers, exclude;

All other values are decomposed by multiple aggregate numbers. Therefore, all values are excluded.

Therefore, the solutions obtained by a are 2 and 2.

Finally, B: I know.

Note: B thinks from the standpoint of a based on its known m value and can get the result of M = 4. The verification is as follows:

M = 4 = 2*2 = 1*4. The sum result is 4, 5. 5 is not in the SS set. Therefore, the result is 2 and 2.

Therefore, the final answer is 2 and 2.

[Reference]

Http://blog.csdn.net/yahohi/article/details/7453005

[Guess a number] Tell A to the two numbers, and product to B to find out what these two numbers are.