Mind Games At Kioloa 2008-YuriyTyshetskiy

From COSNet

Hello, I am Yuriy Tyshetskiy. Currently I am doing research in space plasma physics at Sydney Uni, School of Physics.

Here's another riddle for all to crack:

Two friends-mathematicians who haven't seen each other for a while meet in a park, and sit down on a bench to chat and update on what's going on in their lifes. The following dialogue follows:

- So what's up with you?

- Well, you know, I am married, and have two sons!

- Good for you! I bet they are in some special mathematical school!

- No, they are not going to school yet.

- So how old are they?

- The product of their ages equals the number of pigeons near this bench.

- This information is insufficient...

- The older one is a spitting image of myself!

- Ah, I see, now it's clear!

So how old are the sons?

Good luck :)

Alice, don't loose your sleep over it ;)

You can send your answers to me via email, or post them wherever I can find them, and let me know.

Yuriy.

Some other riddles:

What is the color of your hat?

There was a coup against an emperor in one empire, and all the 100 plotters were caught and thrown into a jail, all in one room. They were announced that they will all be executed the next morning, but the emperor, being a cruel intellectual, wants to give them a chance if they are worthy. The way the execution will be conducted is the following. In the morning, they will all be lined up facing the same way, so that any of them will see everyone in front of him, but not those behind him. Then on each one of them a hat will be put of either white or black color, but in such a manner that none of them will be able to see their own hat (but they can see the hats of those in front of them). Then the executor will start asking each of them one by one, starting from the last one (who can see the whole queue in front of him), what is the color of their hat. A person being asked is the only person allowed to speak at that time, and must only say one word, either "black" or "white". If he correctly names the color of his own hat, he is granted life, otherwise he is executed. Everyone else can hear all the answers, so they are warned that answering anything else beside "black" or "white", or speaking when not asked to, would result in immediate execution of all.

They have till the morning to work out their strategy to save as many as possible. You need to help them!

A hint to get you started: if they develop a strategy by which every odd one of them (starting from the first) names the color of the next person in front, they can guaranteed save at least half of them, possibly more if the 'saviors' are lucky to have the same hat color as the ones they are saving.

But can you find a way to save more?