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Latest Post: May 31, 2010 at 7:26 PM
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Molly Bloom says: (Follow this user)
30 followers

I thought I'd start a thread of clever problems and puzzles. I suggest that people post hints, but don't post answers unless there's a consensus request.

Here's one to begin:

1. Given three line segments, of lengths 1, a, and b, respectively,
draw the line segment which has length a*b.

 

February 28, 2010 at 7:07 PM
William Sanguine says: (Follow this user)
11 followers

I don't think this is particularly relevant to the solution, but here's a proof that it can't be done (by any means whatsoever) without the line segment of length 1.

If a = 100 cm and b = 100 cm, then the desired line segment has a length 100 * 100 = 10,000.

If a = 1 m and b = 1 m, then the desired line segment has a length 1 * 1 = 1.

But the two conditions are the same, since 1 m = 100 cm.  Yet 10,000 cm is not the same as 1 m.  What units is the resulting line segment supposed to have?  So it is unclear what the problem is supposed to mean, or what units are relevant.

If you add the line segment of length 1, you suddenly know what units you are in, and the problem becomes well-defined.

11 comments
 

February 28, 2010 at 7:28 PM
Molly Bloom tagged this post as Insightful.
Arthur Mont tagged this post as Brilliant.
Arthur Mont says: (Follow this user)            In response to William Sanguine
39 followers

William, I just wanted to say that this is a great remark!

 

March 1, 2010 at 12:29 AM
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