Show that all the 1997 sets have one elemen in common. This is a widely known conjecture on the iteration of a map f on the integers.
Nobody seems to know it.
There are four little insects which start from the four vertices A,B,C,D of a square. The speed of all the insects are equal and constant. These questions can be answered without any calculation. These numbers can go from tiny fractions of unity to numbers of the order of a 1 followed by one hundred zeros or even bigger. The player draws one sheet at a time and reads the number on it, and, when he thinks he has found the biggest number of all, he stops.