perplexus.info :: General : Rectangle in lights

Rectangle in lights (Posted on 2004-09-14)

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.	gabbo	2004-09-15 22:58:33
Too easy	bob909	2004-09-14 20:45:11
Alternative Proof	Charlie	2004-09-14 13:37:55
Proof	stan	2004-09-14 13:29:44

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