#21 - Split the Booty Problem

A pirate crew at the end of the day split the booty. The first pirate got 100 gold pieces, and 1/6 of the remaining booty. The second one got 200 gold pieces, and 1/6 of the remaining booty. The third one got 300 gold pieces, and 1/6 of the remaining booty. Ect. The last one only got, what if left from the booty.
At the end, every pirate had the same ammount of gold pieces (from the booty).
How many pirates were there, and how much was the booty.

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Nth pirate gets 100N pieces so there must be 100N^2 pieces in all. This means that the first pirate gets 100N = 100+100(N-1)(N+1)/6. Subtracting 100 form both sides and dividing by (N-1) gives (N+1)/6 = 1 so N=5, each gets 500

#22 - WalK The River Problem

A whole village crowded together at the edge of the lake, they all came for a common purpose.
To see the man who could walk on water.
Many bets were placed, many a dreamer imagined striking it rich on the enourmous sums of money they would win.

The man then took this legendary step from the edge of the bridge onto the water.
He used no artificial tools.
He only had him and the clothes on his back.
Yet he stayed above the surface of the water and could walk around without a thought.

How did he do it?

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the lake is frozen

#23 - Riddle Problem

I am an insect. The beginning of my name is another insect's name. What am i?

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Antlion or beetle