خارش مغزی

Sudoku

The recent Sudoku fever made me rethink the brain itching site! here it is a very neat and good sudoku game, enjoy. BTW, if you don't yet know the game, the objective is to have all rows and columns and highlighted 3*3 squares have every digit from 1 to 9.

It will be great, if you share your records, in the comments section. BTW, if you don't know what Sudoku is take a look at here. Also Spectrum recently had a short article on sudoku solution. It is interesting to find an algorithm that can solve the puzzle in polynomial time, or prove that it is impossible to do so.

سلول انفرادي

5 pirates

updated
This problem contributed by Bahram:

There are 5 pirates who steal 100 diamonds and they want to divide them. They decide to do so as follows:

They create a circle and choose a person by chance so that he assigns diamonds according to his wish. Nevertheless, to have a little more reasoning, they decide to add a second rule: once the division is made, everyone will vote if he is OK with this division or not. If the majority accept the division, then the division becomes final.
Otherwise, they kill the person who made the division, and the next pirate in the circle will do the division with the same rules.

The question is: what is an optimal strategy for the first person,
knowing that everyone would want to maximize his share and that everyone is excellent in logical deduction!

Another thing: when one makes the vote between 5, assuming that he himself votes O.K., 3 negative votes will be regarded as "NO". When one makes the vote between 4, still assuming that he votes O.K., 2 negative votes will be a "NO".