As part of an arithmetic exersise,Mr Strump chooses two different from 1 to 9 te

Question

As part of an arithmetic exersise,Mr Strump chooses two different from 1 to 9 tells abby their product tell Abby their product, then challenges Abby to figure out which two digits he has chosen. After a monent, Abby complains that there could be more than one answer.Realizing that she is correct, Mr.Strump helpfully mentionsthat the sum of the digits is not equal to 10. Abby is then able to correctly deduce the two digits.Explain how it is possible to precisely determine Mr. Strump's two digits based on this story

Explanation / Answer

The story implies that if P is the product then P can be written as product of two digits in more than one way (note we are not giving any preference to the ordering of the pair but treating the pair as a set.Thus it means there is more than one pair whose product if P)

And the rest of the story implies that it is possible to rule all except one when the sum is not equal to 10.So of all the pairs that we got except for one pair other pairs have sum = 10

so apart from the correct pair we must have atleast one of these pairs as possible

{1,9},{2,8},{3,7},{4,6},{5,5} corresponding to products 9,16,21,24,25.

Now only way 25 is product of two distinct digits is 5 times 5.So 25 is not the product.

and only way 21 is product of two distinct digits is 3 times 7.So 21 is not the product.

only way 9 is product of two distinct digits is 1 times 9.So 9 is not the product.

similarly 16 has only one possibility as product of two distinct digits 2 times 8

So product = 24 = 3 times 8 = 6 times 4

So numbers are 3 and 8

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