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Sunday Puzzle-22

User Rating: / 1
Written by Administrator   
Sunday, 30 September 2012
Puzzle courtesy of Barry R. Clarke, columnist for The Daily Telegraph and international puzzle expert

A Pressing Problem

The Department of Silly Ideas has 16 push buttons on the front door arranged in a 4×4 square as shown. Each button is lit in one of the four colours in the rotating sequence: blue, red, yellow, green. When a button is pressed, its colour moves one forward in the sequence (e.g. pushing red makes it yellow, pushing green makes it blue etc.). In addition, three pairs of buttons each  have an internal relationship where one button controls the colour of the  other one but not vice versa. When the controlling button of the pair is  pushed, its colour moves one forward while the controlled button colour moves  one backwards. In the panel shown above, B1 controls C3, A3 controls D1 and  D2 controls B4. So, for example, pressing A3 sends A3 from blue to red and D1  from green to yellow. However, pressing D1 just sends D1 from green to blue. 
Now entry into the department is gained by producing the same colour for all the buttons. What is the smallest number of button pushes required to gain entry?

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Last Updated ( Sunday, 30 September 2012 )
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