As part of an arithmetic exercise Mr Strump chooses two diff

As part of an arithmetic exercise, Mr. Strump chooses two different digits from 1 to 9, tells Abby their product, then challenges Abby to figure out which two digits he has chosen. After a moment, Abby complains that there could be more than one answer. Realizing that she is correct, Mr. Strump helpfully mentions that 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.

Solution

The numbers vary from 1 to 9

Let us choose 2 digits at random, then the digits selected will be minimum when one digit is 1 and other digit is 2 whereas the maximum will be when one digit is 9 and other digit is 8

Hence the number given by Mr. Strump will vary from 2 to 72

Let us suppose there will be two possibilites for some number like number 24

24 can also be obtained as 8 * 3

and 24 can also be obtained as 6 * 4

But after the Mr. Strump second argument second case is not possible since sum of digits will be equal to 10

Hence there is only one possibility left after getting this number for this case

Now take another number let us consider the case when the product is equal to 8

In this case there are two possibilities 1 * 8 and 2 * 4, both of which are possible answer since sum of digits is not equal to 10

Hence there will be some problem still remaining in the solution since there exists multiply solutions for few values