I wonder how many of you took a look at Eric Angelini's two lovely problems which I reproduce here. The first is a wonderful example of a Gardnerian Aha problem. Writing things down would be of no use here, -so much for my theory on the essentiality of pen and paper. The lovely and slightly surprising answer "came to me" a couple of hours after reading the e mail, sitting on a bench in the botanical garden of the town of Lund, Sweeden. Later while trying to get to sleep I worked out the general case where Mr. A brings a liters and Ms. B brings b liters where 2b>a>b. As for the second problem which I just finished, I defy ANYBODY to solve it without doing at least some writing. Remember the answer has to be a number.The paper in front of me contains four drawings, circles, coordinate axes, line segments with various labels, followed by a mess of symbols like x, y ,R, a, pi, integral signs, square root signs. I don't plan to have it framed. David .
A (very) old one I like :
Two Death Valley marathonians friends complete their run together and seek shadow in their tent nearby the finish line.
The first one had prepared a fresh 5-liter tank of water in a cooling box and his friend a similar 3-liter one.
They were about to start drinking when a journalist enters the tent desperately asking for water.
OK, the water is divided into three equal parts -- and drunk.
The thankful journalist insists to pay his share and leaves 8 dollars to be split between the two friends.
How?
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At 07:29 AM 8/6/2007, you wrote:
it's the kind of thing that throws people because it sounds like there's not enough information.
Old Boniface he took his cheer, Then he bored a hole through a solid sphere, Clear through the center, straight and strong, And the hole was just six inches long.
Now tell me, when the end was gained, What volume in the sphere remained? Sounds like I haven't told enough, But I have, and the answer isn't tough!
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There also is a meta-theoretic answer to this puzzle. Assume the puzzle can be solved. Then it must be solvable with a hole of any diameter, even zero. But if you drill a hole of zero diameter that is six inches long, you leave behind the volume of a six inch diameter sphere.
http://www.faqs.org/faqs/puzzles/archive/geometry/part1/
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