Who Knows?

Can anyone guide me in solving this problem?

Quack finds a piece of paper stating the product of two non-zero numbers(the numbers are only from 1 to 8). Mario finds a piece of paper stating the sum of those two numbers. They can't see each other's numbers. They had the following conversation:

Quack: I don't know the numbers.

Mario: I don't know the numbers.

Quack: I don't know the numbers.

Mario: I don't know the numbers.

Quack: I don't know the numbers.

Mario: I know the numbers.

Find the product of the two numbers.

Easy Math Editor

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

Let the numbers be $A$ and $B$ . Assume that $A \leq B$ and make multiplication and addition tables. Then look for ways for particular person to know for sure what the numbers are and if information makes a number impossible, then cross it out and then cross the number in that place out in the other table. If you want the solution or the answer, just reply to my comment.

Jesse Nieminen - 4 years, 10 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$