Gamer say:

Spiral the words Gamer says around in a 3 by 3 board like this:

G A M
Y   E
A S R

On each turn, you may slide one letter horizontally or vertically into the blank space (the square it moved from becomes the new empty square).

You want to rearrange the letters so that the same word is spelled out around the edge, but beginning from one of the edges instead of the corner.

In other words, the board should look like one of these configurations:

Y G A  S A Y  E R S  A M E
A   M  R   G  M   A  G   R
S R E  E M A  A G Y  Y A S

What is the fewest number of turns it takes to do this?

I am not 100% sure but it looks insolvable
Imagine the matrix being colored chess-wise.
Then all the new configurations have an inverse
"parity" color-wise.
Each move imverses the "color" and every letter needs to be moved an odd number of times.
Since the 1st letter stored in the middle square is at some time restored to the same original color- it is moved an even number of times-
therefore contradiction persist.
Having said that I try no more.

ady

Posted by Ady TZIDON on 2004-03-18 15:28:40