Distinct Products?
Tyler chose two distinct integers between 1 to 7 inclusive, and told Perry the product of the two numbers.
Perry says: "I don't know what numbers Tyler choose."
Which of the following could be the number that Tyler told Perry?
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1 solution
Moderator note:
Yes. For completeness, one should show that the options yields a unique factorization of the product of the integers from 1 to 7.
Since 12 = 2 × 6 = 3 × 4 , Perry cannot be certain from this information regarding the two numbers Tyler chose. (They can be either (2 and 6) or (3 and 4)).
All the other options yield a unique factorisation (apart from the order of the factors) if both numbers are integers between 1 and 7:
14 = 2 × 7
8 = 2 3 = 2 × 4 (1 × 8 doesn't work as 8 > 7)
10 = 2 ×5