Logic Thinks!

Logic Level 2

Adam knows the sum of two positive integers while Ben knows their product, but neither knows the two positive integers themselves.

They had the following conversation to find the two numbers:

Adam: "I don't know the numbers."
Ben: "I don't know the numbers."
Adam: "Now I know the numbers!"
Ben: "Now I know the numbers!"

So... what is the value of one of the two positive integers?

Assume both Adam and Ben always tell the truth.

1 2 3 4

View wiki
Winston Choo by Winston Choo , 46, Singapore

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

3 solutions

Zoe Codrington
Jan 22, 2019

The statement made by Adam indicates the sum is not 2 or 3, he would otherwise know the numbers. Ben provides that the product is not a prime, otherwise he would know the numbers. Four as a sum has two values and would by this time reaveal the numbers as 2 and 2. 5 as a sum would not. Six or seven as a sum would have too many possible values to reaveal the number. This means Adam heard 4; at this point he knows the numbers

2 Helpful 1 Interesting 2 Brilliant 1 Confused

why 1 and 6 is not valid ?

A Steven Kusuman - 2 years, 4 months ago

I agree that 4 is a possible number that Adam has heard. However, you still need to show that there is no other possible sum that Adam could have heard, or in the event that Adam could have heard multiple sums, then one of the original integers must be 2.

A better way to present the logic here is through a sum-product grid.

Calvin Lin Staff - 2 years, 4 months ago
Winston Choo
Jan 28, 2019

Firstly, Ben knows that the sum of the numbers is not 2 or 3.

Secondly, Adam knows that the product of the numbers is not a prime number. Somehow after knowing this, Adam knows the numbers.

The product of the numbers is not a prime numbers makes us conclude that the product of the numbers is a composite number. Therefore, neither of the numbers is a '1'.

Note that no matter what Adam had received for the sum of the numbers, only at most 1 of his options had a prime sum. Since after knowing that the correct option did not have a prime product, Adam must have had only 2 options, 1 of them with a prime sum and the other with a composite sum.

Therefore, Adam must had received 4 as the sum of the numbers, as it is the only number which gives exactly 2 options, 1 and 3, 2 and 2.

The correct option does not have a prime product, so the answer is 2 and 2.

0 Helpful 0 Interesting 2 Brilliant 0 Confused
David Lin
Apr 7, 2020

So Adam says that he doesn't know the numbers then the sum was not 2or3 and ben says he doesn't know so the product must not be three then adam know so his sum is four then ben know two so the product is 4 too

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...