Puzzle Nekst 2013 2

Can you not decide whether you should simply enjoy the Christmas holidays or study for your exams?  We have got a solution for you! In this new edition of Nekst we again provide you with a puzzle, a nice combination of relaxing and using your brain. So grab a pen and some paper and enjoy!

In a local village a big lottery will be organized. This lottery will last for 10 days, with prizes getting bigger as the days turn by. All participants have to predict in which order a certain amount of colored balls will be taken out of a vase. On the first day the vase will only contain two different  balls. On the second day, however, it will contain three balls. Each day the number of balls will keep increasing by one, until on the tenth day the vase will contain eleven differently colored balls.

If you predict the order in which the balls are taken out of the vase completely correct on a given day, you will receive an amount of bars of gold equal to the number of that day. For example, if you predict the order correctly on day four, you will receive four bars of gold. Also note that the lottery is free to enter, i.e., there is no participation fee.

A local mathematician also hears of this lottery and one thing strikes him as odd: “The expected amount of gold bars can be written by using only four ones and some mathematical operators.” Can you reconstruct how he did this?

Please send your solution to Nekst@Asset-Econometrics.nl before the 7th of March. A crate of beer or a delicious pie, whichever the winner prefers, will be waiting for whoever has the best (partial) solution. Please note that as before, every recipient of this magazine is eligible to send in their solution, so members of the department are invited to participate as well. Good luck!

Wouter Bieze is the winner of the previous puzzle. As a reward, he can come and pick up a crate of beer or a pie at room E1.10. The solution of the previous puzzle was 20.