A perfect number is a number which is equal to the sum of all its divisors. For example 6 is divisable by 1,2,3 and 1 + 2 + 3 = 6. Can you find another perfect number?

The great Risk tournament is organized again. This year there are 1000 contestants. Each game in the tournament is played with 4 people. After each game, there will be one winner which goes to the next round. In the next round again groups of 4 players are formed. If one does not get an exact multiple of 4 in this way, some of the players in this round are selected randomly. These players can go to the following round automatically. In the end there will be one winner. How many games will be played?

You put two 1 dollar coins on a table, such that they touch each other (see the figure). While you fix the lower coin with your finger, you will turn the upper around it (without slipping). Somewhat later the moving coin will be back in his original position. How many rotations on his midpoint did the moving coin make?