This is a relatively simple puzzle from fivethirtyeight.com, a site from which I have posted many puzzles in the past. Variations of such puzzles have been posted in the past. I would encourage parents to try this with their children.

Two intelligent, honest students are sitting together at lunch one day when their math teacher hands them each a card. “Your cards each have an integer on them,” the teacher tells them. “The product of the two numbers is either 12, 15 or 18. The first to correctly guess the number on the other’s card wins.”

The first student looks at her card and says, “I don’t know what your number is.”

The second student looks at her card and says, “I don’t know what your number is, either.”

The first student then says, “*Now* I know your number.”

What number is on the loser’s card?

As always, please send your answers as comments within the blog (preferred), or send an e-mail to alokgoyal_2001@yahoo.com. Please do share the puzzle with others if you like, and please also send puzzles that you have come across that you think I can share in this blog.

Happy guessing!

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*Related*

Possible combinations are:

12 : (3,4) , (4,3) , (6,2) , (2,6)

15 : (3,5) , (5,3)

18 : (3,6) , (6,3) , (9,2) , (2,9)

– When first student says, “I don’t know your number”. It means he has 2,3 or 6. Because if he had 4,5,9 he could easily guess the number on other student’s card.

– Now, we have following possible cases, (2,6) , (2,9) , (6,3) , (6,2) , (3,4) , (3,5) , (3,6)

– When second student says, “I don’t know the your number either”. It means that he has 6.

– Now, first student can easily guess the number on second student’s card, which is 6.

So, the number on looser’s card is 6

6

After first student comment, we know he has 2,3 or 6

After second student comment, we know hr has 2,3 or 6

So the possible combinations are (2,6) and (3,6)

If the first person had 6, he would not know the second person’s number

So second person has 6

6