Masao Kitamura

Three men decided to split the cost of a hotel room. The hotel manager gave them a price of $30.

The men split the bill evenly, each paying $10, and went to their room. However, the hotel manager realized that it was a Wednesday night, which meant the hotel had a special: rooms were only $25. He had overcharged them $5!

He called the bellboy, gave him five one-dollar bills and told him to return it to the men.

When the bellboy explained the situation to the men, they were so pleased at the honesty of the establishment that they promptly tipped the bellboy $2 of the $5 he had returned and each kept $1 for himself.

So each of the three men ended up paying $9 (their original $10, minus $1 back) totaling $27, plus $2 for the bellboy which makes $29. So where is the missing dollar?

You have two ropes that each burn for 1 hour end to end, but at varying rates.

You have a lighter. You cannot cut the ropes (and doing so wouldn’t help, since they burn at unknown rates and you only know total burn time).

How do you measure 45 minutes?

You have 8 bricks, but one of them is lighter than the rest.

You have a balance you can only use twice.

How do you find the lighter brick?

Of three options, you have a 1/3 chance of picking the “right” option.

If you pick one at random, then a single “wrong” option is eliminated, should you switch and why?