The Guardian today posted three very difficult math problems selected from the archives of Pythagoras magazine.
One puzzle asks you to divide the shape above into two identical shapes. I suppose a trivial answer would be to divide it in the plane on which it exists, but there must be a more elegant solution.
Then there is the Dollar Bill problem:
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?And a Huge Pie problem:
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?The last one could be solved by brute force, but a proper answer requires a mathematical explanation.
I don't have answers for you; unless readers post solutions in the Comments, you'll need to go to The Guardian.