15 Jun '08 11:36

This problem is very similar to the last one. Hopefully many of you will be able to solve it!

Suppose we have the bottom left hand corner of a chessboard, and this chessboard extends up and to the left forever. Call the bottom left corner (0,0), the one to the right of that (1,0) and the one above that one (1,1) etc. You get the gist. Think of the first quadrant of a cartesian plane, but only with integers.

Now we have three blobs living on this chessboard, one at (0,0), one at (1,0) and the third ad (0,1). These blobs reproduce by splitting up. When a blob splits up, one half of it moves up one space (this space must be empty) and the other half moves right one space. The space of the original blob is now empty. This happens to exactly one of the blobs each second. The blobs cannot move in any other way.

In other words, a "move" consist of taking:

a blob on (x.y)

an empty space at (x+1,y)

an empty space at (x,y+1)

and turning it into:

an empty space at (x,y)

a blob on (x+1,y)

a blob on (x,y+1)

Make sense?

Now these three starting blobs live in their cosy home. The home consists of (0,0), (1,0) and (0,1). What is the minimum number of seconds it will take for the blobs to completely vacate their home?

Suppose we have the bottom left hand corner of a chessboard, and this chessboard extends up and to the left forever. Call the bottom left corner (0,0), the one to the right of that (1,0) and the one above that one (1,1) etc. You get the gist. Think of the first quadrant of a cartesian plane, but only with integers.

Now we have three blobs living on this chessboard, one at (0,0), one at (1,0) and the third ad (0,1). These blobs reproduce by splitting up. When a blob splits up, one half of it moves up one space (this space must be empty) and the other half moves right one space. The space of the original blob is now empty. This happens to exactly one of the blobs each second. The blobs cannot move in any other way.

In other words, a "move" consist of taking:

a blob on (x.y)

an empty space at (x+1,y)

an empty space at (x,y+1)

and turning it into:

an empty space at (x,y)

a blob on (x+1,y)

a blob on (x,y+1)

Make sense?

Now these three starting blobs live in their cosy home. The home consists of (0,0), (1,0) and (0,1). What is the minimum number of seconds it will take for the blobs to completely vacate their home?