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Nir Dahan Inner circle Munich, Germany 1390 Posts |
Since I can't solve any of the word puzzles you guys post here is an oldie that is also a beauty since it is so counter-intuitive.
you have as many bricks as you wish with dimensions 1x1xL. what is the maximum overhang that can be created by piling them up one on top of the other. you cannot put some bricks on the other side to balance the weight of the overhang! just pile them up to one side and measure the distance from the edge of the bottom most brick. according to feeling alone - do you believe it is possible to extend the edge of the top most brick by more than the brick's length L? i.e. the entire brick will "clear" from the bottom most brick. that is a beautiful problem that was given to me in one of the early calculus/physics classes. the solution can be easy found using google... Nir p.s. if any one of the regulars (stan, jack, tomas, george etc.) can find a nice way of explaining this please share it - I have a hard time explaining the solution in a simple way... |
TomasB Inner circle Sweden 1144 Posts |
I think the best way of explaining it is that the series describing the overhang is a harmonic series (a/2 + a/3 + a/4 + ... ) which, most know, doesn't converge. In other words, no matter what overhang you say, I will eventually pass it by just adding more terms to that sum.
When I do tradeshows with work we always have parquet pieces lying around (we develop wood scanners) and I hand visitors four pieces and the puzzle is to put them over the edge of the table in a lengthwise stair formation and, if possible, get the top one to totally clear the table's edge. /Tomas |
Nir Dahan Inner circle Munich, Germany 1390 Posts |
Tomas,
I think the problem is how to show intuitively that the overhang is described by the harmonic series (or half the harmonic series if I remember correctly) Nir |
TomasB Inner circle Sweden 1144 Posts |
Nir, the solution to that is actually how I stack the four pieces for the stunt:
Hold all four pieces square and push the top one over until it is on the verge of falling. You will see 1/2 of the piece below it. Next move the top two pieces at a unit until they are on the verge of falling off the third one from the top. You will clearly see 1/3 of the piece below them. Just repeat this by moving the top three as a unit until they almost fall then move all for as a unit until they almost fall off the table. The top one will cleary be free of the table and the ratios of extension will give them a hint that it is actually a harmonic series. Starting with the lowermost and placing one at the time on top is close to impossible to succeed unless you already know the ratios to extend them. Great puzzle I think as that is usually the order people start trying to put them, starting from bottom and up. /Tomas |
Nir Dahan Inner circle Munich, Germany 1390 Posts |
Could be a nice carnival game too.
we just have to find a way to cheat with it. maybe a brick which is not really symmetrical... Nir |
leonard Regular user North Carolina 148 Posts |
Tomas,
You threw me off the track. I had to go back and check my math. I believe that when you slide the top two pieces as a unit, you only expose 1/4 (not 1/3) of the piece below them. The actual series then becomes 1/2, 1/4, 1/6, and 1/8, which totals to 25/24 (1.041) for four blocks. Can you arrange three blocks to get a full block of overhang? How about four blocks to get 1.168? regards, leonard |
TomasB Inner circle Sweden 1144 Posts |
Sorry about my error, Leonard. As Nir wrote earlier it's half the harmonic series, which is what you wrote and what I meant.
/Tomas |
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