2. Does Pang Juan know about Sun Bin? First, he explained that b is not the product of two prime numbers. In other words, there are at least three prime factors in B, which will lead to Sun Bin's confusion. Since an even number greater than 6 and less than 200 can be expressed as the sum of two prime numbers (the famous 1+ 1 question), then Pang Juan must know that A is an odd number, otherwise it is possible that A can be expressed as the sum of two prime numbers, so Pang Juan can't claim to know that Bin Sun doesn't know (how it sounds so awkward). From our point of view, we can infer two points: A is an odd number, and there must be an odd number when splitting, so B must have a prime factor of 2, and A-2 is a composite number (only 2 is an even number, otherwise there must be an even number greater than 2, and the product of two numbers must have at least three prime factors); The greatest prime factor of b must be less than 50, otherwise Sun can determine what these two numbers are, and Pang dare not claim to know that Sun doesn't know. It can be inferred from the fact that the maximum prime factor is less than 50 that the value of A must be less than 53+2=55(53 is the smallest prime number greater than 50), because any number greater than or equal to 55 can be expressed as 53+(55-X). In this case, Sun Bin must know how to split B-of course, Sun also knows this analysis process, so what we can think of, with the wisdom of these two, of course, can be thought of. Now Sun Bin also knows this situation. He knows a B more than us.
3. After Pang Juan made his first speech, Sun Bin got the message that A is an odd number less than 55 and greater than 5, and A-2 is a composite number. Sun Bin said "I know" after receiving this information. For our third party, it provides some information. Because these two numbers are odd and even, there are only three possibilities for Sun Bin to make sure that he knows these two numbers. One is that A is the sum of an odd prime factor and the power of 2 (the power is greater than 1), and the other is that A is the sum of an odd prime factor (obviously there can be only one factor) and another even number-both of which can be determined by Sun Bin. Another possibility is that Sun Bin can only determine these two numbers when there is only one case of all splits of B among the possible values of A. ..
4. When Sun Bin said "I know", Pang Juan understood why Sun Bin said "I know", because he also knew that only the above three situations could guarantee Sun Bin to know. Then Pang Juan judged what Sun Bin was talking about according to his known value of A, and got the only possible value.
The possible values of a are as follows: 1 1, 17, 23, 27, 29, 35, 37, 4 1, 47, 5 1, 53.
When the maximum odd prime factor of B is more than half of 53 and less than 53, that is, when the maximum odd prime factor of B is 29,31,37,41,43,47, it is obvious that A is greater than 29+2=33. At this time, A can be divided into a big odd prime factor and the sum of an even number, or a power of 2 (power greater than 1) and the sum of an odd prime number, and there is only one way to split A, so that Pang Juan can determine which two numbers it is, that is to say, he can say "I know". First of all, some possible values of a are excluded without considering the above third case.
Rule out one by one
Exclude the unique11= 2 2+7 = 2 3+3 (there are two cases that satisfy the first condition above). 17 = 2 2+13 = 2 3+3 * 3, make an appointment first if possible. Exclude 29 = 2 2+5 * 5 = 2 3+3 * 7 = 2 4+13. If possible, first keep 35 = 2 2+31= 2 3+3 * 3 = 2 4+65438. Exclude 41= 2 2+37 = 2 3+3 *1= 2 4+5 * 5 = 2 5+3 * 3, and keep 47 = 2 2 2 2+43 = if possible. First, keep 51= 22+47 = 23+43 = 24+5 * 7 = 25+19, and exclude 53 = 2 2+7 * 7 = 2 3+5 * 9 = 2.
Thus, the reserved values of A in the first round are: 17, 29, 4 1, 47, 53. At this time, from Pang Juan's point of view, although only one of the last three numbers may be decomposed into the sum of a power of 2 and an odd prime number, it may also be decomposed into the sum of an odd prime number (27=53/2) less than 53 and greater than 27 and another even number. In both cases, Sun Bin can determine these two numbers, but Pang Juan can't, so these three numbers are also excluded. So the remaining two numbers are 17 and 29, which is a possible value of a.
Then, the sum terms of 17 and 29 are split, and it is found that when 17 is split, only the sum of all other b product terms is split into the possible values of A in the case of 4 and 13, while other splits may have two of the above values of A. After splitting 29, it is found that the product b without 29 is split into numbers and the sum after product splitting is. Therefore, the only eligible A value is 17, while the split values are 4 and 13.