hundred monkeys

There are 100 monkeys in a zoo and they feed them 1600 bananas.
Can you show that at least 4 monkeys get the same number of bananas, no matter how the monkeys distribute them among each other?

via DerSpiegel


At breakfast I proved the famous theorem of Pythagoras (again). I do this every now and then, as well as other quick calculations, e.g. deriving relativistic time dilation, average distance traveled of a random walk, ground state of the harmonic oscillator, etc. mostly to check that my brain is still working properly.

But this time it led to the question how many times this theorem has been proven already and I suspect the answer is several billion times. (I am assuming most kids have to do this at least once, but I am not sure if it counts if the teacher does it and they just watch.)
In other words the probability is very low that Pythagoras got it wrong. However, I cannot rule out that I already lost my marbles and, plagued by a combination of Alzheimer's and schizophrenia, only imagine that I calculated correctly and in reality it is all wrong.
But how would one estimate the probability for that? (*)

(*) Just another attempt to shake the Platonist worldview a little bit.

having a good time

"He’s a great guy. Smart. Strong. Loves holding my hand.
People don’t realize he loves holding my hand. And that’s good, as far as that goes.
I mean, really. He’s a very good person. And a tough guy, but look, he has to be. I think he is going to be a terrific president of France. But he does love holding my hand.
Same thing happened to Hitler. Not for that reason, though. Hitler wanted to consolidate. He was all set to walk in. But he wanted to consolidate, and it went and dropped to 35 degrees below zero, and that was the end of that army.
But the Russians have great fighters in the cold. They use the cold to their advantage. I mean, they’ve won five wars where the armies that went against them froze to death. [crosstalk] It’s pretty amazing.
So, we’re having a good time. The economy is doing great."


Yes, I agree this is "pretty amazing". But I do have a question about the "five wars".
Everybody knows about Adolf and Napoleon - perhaps he even knows about the Great Northern War and the Crimean War (I doubt that). But what was the fifth war?

added later: " “And then you call places like Malaysia, Indonesia, and you say, you know, how many people do you have? And it’s pretty amazing how many people they have.” NYMag