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November 30th, 2012, 05:30 PM   #1
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A even more tricky question

More than a year ago, I posted the "A very tricky question" post on this site, to share the fun I had.

Let's look at the question first

I am not sure if it should be included in this section, if not, it is ok for moderators to remove it because this problem might be too hard for middle school students but the technique school students should know, it is just hard to think it that way.
The question is:
"A (a person) had 2 Integers in his head between 2 and 99 inclusive, he told B (a person) the sum of two numbers, and told C (of course, another human being) the product of those two numbers, and then B and C had this following conversation:

C: I don't know the numbers.
B: I know you don't know the numbers, I don't know it either.
C: Then I know the numbers.
B: Then I do too!

What were the two numbers?"
This is from one of my oldest posts, the answer to this question is 4 and 13 after a complex thought, now I am going to expand the question . What will the solutions be if the restraints are between 2 and 1000 inclusive?

The answer is 4 and 61. Will there be more possible solutions? and does the case 4 and 13 still work when we expand into 2 and 1000 inclusive?

I thought yes because in the final step I believe the sums will still all cancel out... according to my notes , and leave only 13 and 4 for the sum of 17 set.

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