There are 16 buttons in a four by four array. Each button has a horizontal arrow, pointing left or right, and a vertical arrow, pointing up or down. Initially, all arrows point towards the center of the array. In the below diagram, U is up, D is down, R is right, and L is left.

DR DR DL DL
DR DR DL DL
UR UR UL UL
UR UR UL UL

When you press a button, all other buttons in the direction of its horizontal arrow flip their vertical arrows, while all other buttons in the direction of the vertical arrow flip their horizontal arrows. The following diagram is the result after pressing the button in the upper left corner.

DR UR UL UL
DL DR DL DL
UL UR UL UL
UL UR UL UL

Find the least number of button presses required to get to the position in which all arrows point away from the center of the array.

(In reply to re(2): Solution by Penny)

"All arrows point away from the center of the array" is not meant to be a trick.  It means the complete reversal of the original position, in which "all arrows point towards the center of the array."  Yes, recall that each button is composed of not one, but two arrows.

DR DR DL DL    UL UL UR UR
DR DR DL DL to UL UL UR UR
UR UR UL UL    DL DL DR DR
UR UR UL UL    DL DL DR DR

There is a solution, but as far as I know, it requires more than a few moves.  Might I suggest narrowing the search space by considering the symmetry of the starting and ending positions.

Posted by Tristan on 2006-11-05 19:08:33