Cool math problems

It’s been forever since I’ve done a math post. Here are two problems which I find very cool. In both of them one has to use the fact that someone can or cannot solve a problem at a given time as the extra piece of information needed to arrive at the solution. I don’t know any other similar problems.

In order to spare the delicate sensibilities of some of the readers, the problems are below the fold. Feel free to share ideas/solutions in the comments. In a few days I’ll post solutions.

Problem 1. Two mathematicians Alice and Bob were talking about their children. Typically absent-minded Alice had remembered that Bob had three children, but had forgotten their ages. So she asked Bob how old his children were. In true mathematical (read abstruse) fashion Bob answered:

“The product of their ages is 36 and the sum of their ages is the number of the pink house across the street.”

“I still don’t know their ages,” replied Alice.

“Well,” Bob added. “The oldest one is a really giften theremin player.”

Alice was then able to work out the kids’ ages. Are you?

Problem 2. Cory and Deyan are two mathematically gifted kids, who have just met at Deyan’s house. Deyan wanted to know where Cory lived. As Cory was Bob’s son, he told Deyan:

“The number of my house has two digits. If you subtract from it the number, but the digits reversed. (eg. 52-25) you’ll get the number of your house.”

“Trivial,” said Deyan, and in no time he worked out Cory’s house number. Can you do the same?

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