What is Sum of Those Two Number

Number Theory Level 2

The following is a conversation of A and B.

A : I thought of two distinct one-digit numbers. Can you guess the sum of these two numbers?

B : No, can you give me a clue?

A : The last digit of the product of the two numbers is your house number

B : Now i know the sum of the two numbers.

What is the sum of the two numbers?

1 solution

Mr. India
May 15, 2019

Unit digit of product	Possible distinct number combination
$1$	$3×7$
$2$	$1×2,3×4,8×9...$
$3$	$1×3,7×9$
$4$	$1×4,3×8,6×9...$
$5$	$1×5,5×3,5×7...$
$6$	$1×6,4×9,2×3...$
$7$	$1×7,3×9$
$8$	$1×8,2×4,3×6...$
$9$	$1×9$

Only 1 and 9 have single combination and sum of both combinations is 10

So, if house number of $B$ was either $1$ or $9$ , then only he could have known the sum of the numbers which is $\boxed{10}$