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.
Apparently not the solution, as what is required is the complete reversal of the starting position:
UL UL UR UR
UL UL UR UR
DL DL DR DR
DL DL DR DR
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Original post:
Minimum number of buttons to push: 6
Initial array:
DR DR DL DL
DR DR DL DL
UR UR UL UL
UR UR UL UL
(a) Push button at (0,0)
Then the array is:
DR UR UL UL
DL DR DL DL
UL UR UL UL
UL UR UL UL
(b) Push button at (0,2)
Then the array is:
UR DR UL UL
DL DR DL DL
UL UR UL UL
UL UR UL UL
(c) Push button at (2,1)
Then the array is:
UR DL UL UL
DL DL DL DL
UL UR DL DL
UL UR UL UL
(d) Push button at (3,1)
Then the array is:
UR DR UL UL
DL DR DL DL
UL UL DL DL
UL UR DL DL
(e) Push button at (1,1)
Then the array is:
UR DR UL UL
DL DR UL UL
UL UR DL DL
UL UL DL DL
(f) Push button at (3,1)
Then the array is:
UR DL UL UL
DL DL UL UL
UL UL DL DL
DL UL DL DL
and none of the arrows is pointing at the center, and in that sense "all arrows point away from the center of the array."
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Note: I found the strict reverse of the given starting position
impossible to achieve from that starting position by pressing buttons sequentially:
UL UL UR UR
UL UL UR UR
DL DL DR DR
DL DL DR DR
Edited on November 5, 2006, 9:00 pm
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Posted by Penny
on 2006-11-05 04:47:08 |
Solution
