Olifante's Lair

Bluebirds and blackbirds

Another great puzzle:

A collection of bluebirds and blackbirds sit on a wire.
1. There is at least one bird of each type.
2. Each pair of birds with 15 or 20 birds between them are the same color.

What is the largest number of birds that could be sitting on the wire?

How many rings?

While digging through some old papers, I found a copy of what is probably my favorite puzzle. I googled it but couldn't find any references, so I'm posting it. If anyone knows who authored it, let me know.

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There are 31 people around a table, each with a square of a given colour on the forehead. Each one must find out what his own colour is, without communicating in any way with the others.

Successive rings are sounded, and each person must leave the table on finding out what his colour is.

• On the first ring, four persons left.
• On the second, everybody in red left.
• On the third, no one got up.
• On the fourth, at least one person got up.

How many rings were sounded after that one?

Remember that everybody passed the test.

Additionally, the leader and his sister left before the last ring (the one that empties the table) and wore different colours.