Can you solve it? Pythagoras’s best puzzles

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Three teasers from the vaults

Hi guzzlers,

The most famous theorem in maths is named after the Greek thinker Pythagoras. So is the most famous recreational mathematics publication in the Netherlands.

Pythagoras Magazine was founded in 1961, and to celebrate its half century it recently published a selection of its best brainteasers in English. Ive selected three of them here, in increasing order of difficulty.

1) Dollar bills. In a bag are 26 bills. If you take out 20 bills from the bag at random, you have at least one 1-dollar bill, two 2-dollar bills, and five 5-dollar bills. How much money was in the bag?

2) Yin and Yang. The Yin-Yang symbol is based on the figure below, bordered by three semi-circles. How can you divide this shape into two identical shapes?

Big
Big yin

3) Huge pie. A huge pie is divided among 100 guests. The first guest gets 1% of the pie. The second guest gets 2% of the remaining part. The third guest gets 3% of the rest, etc. The last guest gets 100% of the last part. Who gets the biggest piece?

Ill be back later today with the solutions.

NO SPOILERS PLEASE

I set a puzzle here every two weeks on a Monday. Send me your email if you want me to alert you each time I post a new one. Im always on the look-out for great puzzles. If you would like to suggest one, email me.

Thanks to the editors of Pythagoras Magazine for todays puzzles. You can check out more of them in Half a Century of Pythagoras Magazine.

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Read more: https://www.theguardian.com/science/2017/jun/19/can-you-solve-it-pythagorass-best-puzzles