Puzzle of the week: duel for gummy bears
Paul and Paula play for gummy bears. Their number guessing game seems to offer both big odds of winning. Or is there perhaps a strategy that gives a player an advantage?
Two people and a big pile of gummy bears. What can go wrong? So much. In our case, both Paul and Paula want to have as many gummy bears as possible. So that there is no dispute, the two have come up with a game that regulates the distribution of gummy bears.
Paula looks for any two integers, about 288 and -33, and writes them on a piece of paper. The only condition: The numbers must be different. She places the two pieces of paper on the table with the backside up. Paul can not see the numbers.
Then Paul turns over one of the two pieces of paper and sees one of the numbers chosen by Paula. Paul has to decide: Is this number greater than the number not yet revealed? Or is she smaller? If he is right, he gets a gummy. If he is wrong, Paula may take one.
Paul could throw a coin every time and say headfirst: "The number revealed is bigger". And in number: "The number is smaller." Then he would have as much chance of winning a gummy bear as Paula.
But maybe there is a strategy that could give Paul an advantage? What do you mean?