/sci/ - Science & Math

[Anonymous No.3770919]

No responses yesterday, I believe it sank to the bottom of the board before catching the eye of anyone interested ; so I'll repost it : This is chess/algebra problem time!

The first part of the problem is about a chess grid. How many POSSIBLE (be careful about bishops!) different positions is there at a given time, If :
- pawns can't stray further than 3 columns of their initial column?
- pawns can go all the way to 6 columns to the left or the right?
- pawns can't take other pieces diagonnally?


Second part : What is the probability that the same position arises in two consecutives games of 50 moves? 100 moves?

Third part : how many different chess game can you play, assuming that you can't go back from one position to the previous one (i.e repeating one move)?
Note : chess rules actually allow up to three repeating positions before the game is declared null.


Good luck!

[Anonymous No.3770938]

>>3770919

i prefer 'blitz chess'.

[pascal !n5Z3VuZapw No.3770980]

For peice positions, are we counting pawns that turned into other peices, as limited by your pawn limitations, or free to go anywherr?

[Anonymous No.3771180]

>>3770980
pawns are pawns. If they are promoted, they are no longer pawns.

At first, let's assume no promotion was involved.