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In the monthly (?) publication of Tau Beta Pi, there used to be brain teasers.

Some of them were really good (they really messed up your brain),

Snehal, are still enjoying them ?

Since the users on this site are mostly techies, maybe a forum could be set up for Brain Teasers.

But here's one for the serious programmers.

Suppose you have a hollow aluminum cylinder (open at the top), say 'x' inches ID. Place a solid (right circular) aluminum cylinder, dia 'y' aprox. half of 'x', in the center of the hollow one, flat face down.

Now gently pour mercury into the hollow cylinder, without wobbling the sold one. At what level of mercury will the solid cylinder just rise ?

Usefull formulas :

A=pi*r^2, V = A* h, W = mg

Buoyant force = weight of the fluid displaced.

What bells & whistles need to be put into the program ?

Wow, not a single taker!

I’ll venture a reply.

Height of mercury = Length of solid aluminum cylinder x specific gravity of aluminum / specific gravity of mercury

Diameters and areas don’t come into it.

If I’m right, I’m clever. If I’m wrong, it’s a silly problem.

Here’s one on probabilities, requiring only simple logic, no maths.

Three bandits, A, B & C, are arrested and placed in separate cells. The king wants to make an example of the case and announces that whoever of the 3 has committed the most serious offences will be executed. To find out who this is, they will be tried in two’s, one against the other.

Bandit A makes friends with the guard and asks for info on the trials. The guard tells him, “You have not been tried yet. But B has been tried against C and had the more serious offences. So C gets to live, and tomorrow you will be tried against B to see which one of you who will be executed.”

Now let’s see the probabilities. Without the guard’s info, bandit A had a chance of 1/3 to be executed. But now that we have the guard’s info, what is the new probability that A will be executed? Is it 1/3, ½ or something else, and if so what?

I've always been terrible at these types of things, but is it 1/2?

@ mopar man

You already get some credit for venturing a reply, which is more than others have done.

But I won’t say yet whether it’s right or wrong, so as to give more people a chance.

Good idea. I was thinking it would be one of those "answer first, then ask a question" type threads. Luckily I was wrong. I had to wait for one that I could at least attempt, so when you posted yours I was happy. (I haven't even taken Chemistry yet... XD)

It makes sense that it is 1/2, but it feels too easy to come to this solution, so it makes me feel like it cant be correct.

It is hardly a silly problem.

It is from one of the best Physics books in the world.