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You don't have to take all combinations to work this one out. It is based on the following:

If a number is the product of two primes, then you know their sum.


A: I don't know the sum. So the number is not the product of two primes. One of the numbers must be 4, 6, 8, 9 or 10.

B: I knew that. This is the biggest clue! If the sum can also be a sum of two primes, then B would not be absolutely sure that A does not know the numbers eg if B's sum was 6, then it could be that A's product is 9=3x3, from which A could immediately deduce the two numbers. So the fact that B knew that A did not know the sum limits the sum to be 11. Every other number under 14 is the sum of two primes: 4=2+2, 5=2+3, 6=3+3, 7=3+4, 8=3+5, 9=2+7, 10=3+7, 12=5+7, 13=2+11.

So the possibilities are 2 9, 3 8, 4 7, or 5 6.

B: The sum is less than 14

A: I knew that. This implies that the product cannot be factored out into two numbers whose sum is larger or equal to 14. Now the largest sum that the factors can add to is when we take a large and a small factor. This eliminates 3x8=24=2x12, which allows 2+12=14;v or 4x7=28=2x14 with 2+14>14; or 5x6=30=2x15, 2+15>14; leaving only 2x9=18=3x6. So the numbers are 2 and 9.

hi dude ididnt get the solution can u pls eloborate it.

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