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Rectangle in lights (Posted on 2004-09-14) Difficulty: 3 of 5
Imagine an array of 3 x 7 lights. Lights can be on or off. Show that no matter which lights you turn on or off, you will always be able to find four lights forming the corner of a rectangle, either all on or all off.

  Submitted by Federico Kereki    
Rating: 3.0000 (5 votes)
Solution: (Hide)
Obviously, in any column there will be at least two lights with the same status -- say 0=off, 1=on. There are thus six possible configurations: 00x, 0x0, x00, 11x, 1x1, and x11. ("x" stands for "don't care".)

As there are seven columns, at least one configurations must be repeated, and we thus get our rectangle.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Still fun though.gabbo2004-09-15 22:58:33
Too easybob9092004-09-14 20:45:11
SolutionAlternative ProofCharlie2004-09-14 13:37:55
SolutionProofstan2004-09-14 13:29:44
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