October 29, 2013
Problem of the Week
for Tuesday, October 29, 2013
Your eccentric uncle Pascal brings you three presents every year for your birthday but he shows you them one at a time and you only get to choose one as your gift. When shown the first present, you can decide to accept it or pass over it in order to see the next present. You can likewise pass over the second present in order to see the third. The trouble is that once you pass over a present, you can not return to it, even if you decide that you like it best. This means that if you pass over presents one and two, you are stuck with present three. Given that Pascal offers his presents in a random order, what strategy can you use in order to be able to select the present that you think is the best on roughly half of your birthdays? Describe your procedure.