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.

Tristan, this is great. Would make a good electronic game. Market it for cell phones!

Well?  A thought.

I have to get the thought out of my head that only one attribute in horizontal and vertical directions change. 

I keep coming back to look at this with the thought that both attributes change; but that would be a different problem.

Posted by brianjn on 2006-10-29 21:43:03