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Castle


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#1 rookie1ja

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Posted 30 March 2007 - 04:29 PM

The Castle - Back to the Logic Puzzles
A square medieval castle on a square island is under siege. All around the castle there is a square moat 10 meters wide. Due to a regrettable miscalculation the raiders have brought footbridges, which are only 9.5 meters long. The invaders cannot abandon their campaign and return empty-handed.
How can the assailants resolve their predicament?

This old topic is locked since it was answered many times. You can check solution in the Spoiler below.
Pls visit New Puzzles section to see always fresh brain teasers.


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#2 jahash

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Posted 02 May 2007 - 09:19 PM

Could you not also lash 2 footbridges together with a slight overlap to make one longer one?
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#3 Paige's Mom

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Posted 03 May 2007 - 04:13 PM

Could you not also lash 2 footbridges together with a slight overlap to make one longer one?




But then the integrity of the footbridge would be compromised and nobody could guarantee your safety.

Haven't you read Stephen King's "Eye of the Dragon" and the "tension breaking point" theory?
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#4 Skumbag

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Posted 14 May 2007 - 09:31 PM

Lash two of them over a third one underneath for support:

11111111112222222222
(space)3333333(space)

Having said that, if they have enough wood for all this, why can't they make 10m+ footbridges?
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#5 fosley

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Posted 15 May 2007 - 12:11 AM

I've got an idea: swim. Or put floating barrels on the water with the 9.5m planks firmly attached so they float atop the barrels. By attaching 10 or 20 in a row, you could safely walk across the middle without falling over.

Another solution I've actually done:
Place one board so it's sticking out 1.5 meters over the edge. It has 8 meters still on flat ground. Now, have 1 man stand on the end furthest from the moat. Because of mechanical advantage, you can put the weight of ~5.33 men on the other end of the board (8 / 1.5 ~= 5.33 ). Carry a board vertically 1 meter out, then drop the top end so it swings down and lands on the opposite edge. Set the close edge so .5 meters of the second board is resting on the first board, and there will be .5 meters resting on the opposite side, with the remaining 8.5 meters bridging the gap. I'm not sure of the exact physics, but I know that the maximum mechanical disadvantage for the guy holding the board down is 10:8, or 1.25, and that would occur when someone was standing at the very opposite edge of the moat. So 2 guys on the end away from the castle would be sufficient for 1 guy to cross the bridge.

Once the first guy is across, you have a few options:
1. Send a second guy across (total of 4 guys), reverse the boards (so the far board has 1.5m sticking over the moat and the near board covers the remaining 8.5 meters), then walk the remaining 2 guys across, bringing the second board with them. (This is the method I used, because the objective was to cross the gap and bring the boards with us so we could cross the remaining gaps.)
2. Pull both boards so that .75 meters are sticking over the moat and use a 3rd board to cover the remaining 8.5 meters. Now, you have a worst case advantage of 1.75:1, because you have 8.75 meters on land, and if the load is more than 5 meters from your edge, the other board is taking the extra load. (This is basically the same setup as Skumbag's, except I'm using weight instead of lashing to keep things from falling.)
3. Pull both boards so 5 meters is over the moat and the remaining 4.5 meters is on dry land on either edge. The disadvantage is now 1.11:1, so 1 big guy holding some heavy-ish stuff could get smaller guys across.

You could also put something very heavy on the end to support more than 2 people crossing at a time (such as an anvil or large tank filled with water). Your wieght-over-the-water would ultimately be limited by how much stress the boards could take, but you could always roll heavier objects across multiple boards at once to distribute the load.

The disadvantage of my method is the requirement to leave something heavy on the ends while people are crossing, but it has the advantage that the army can breach the gap anywhere along the moat. I would guess that for any reasonable army, the advantage would far outweigh the disadvantage. Of course, I'd also guess that a reasonable army could make 10+ meters boards.

Note: Umm. I made a mistake in my counting somewhere, and don't feel like fixing it at the moment. However, the concept remains valid. Edit: the mistake is on the picture, frame 4. It should read "8.5 m", not "7.5 m".

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#6 Veracity

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Posted 18 May 2007 - 04:49 PM

lol, I LOVE IT. That was not only a very wise discovery on how to gain access to the other side, but a cool little diagram you built to explain it better.. I like the art work..lol Plus, your way does not leave any Gaps and is a straight shot across. I suppose Rookies answer does not leave any gaps either, but would require you to walk in from the side and turn. Either way, Both very cool answers... I, on the other hand, would hire a Cuban to carry me across!

(I can say that, I'm Cuban..lol)
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#7 Aaron Burr

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Posted 22 May 2007 - 12:39 AM

a simple solution is to build the 9.5 foot bridge and jump the other .5 meters (or 1.5 feet) Unless of course we are assuming the bridge will not hold without a base on the other side. This could easily be solved with a simple rope support system; attached the ropes to the end and periodically along the edge of the bridge to support it. The ropes would be run up to a tree, that happens to be near by, and then fastened to the ground.
-Remember today is the tomorrow you worried about yesterday.
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#8 sk8erfou

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Posted 11 June 2007 - 09:52 AM

well the problem with jumping is... the bridge would fall over as soon as you reached the end... the more logical sence would be like in a^2+b^2=c^2... would be to turn it on its side so the diagonals were touching both sides... assuming of course these were soldiers and not tight rope walkers and the bridge had width
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#9 yar divad

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Posted 25 June 2007 - 04:02 PM

You guys are missing a key aspect of this scenario...the castle is on an island. If you just make a canal linking to the ocean, the moat will drain itself and you won't even need to bother with foot bridges.
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#10 undeniable

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Posted 27 June 2007 - 08:12 PM

I would just put 1 bridge across the corner and the other from the middle of that bridge the edge of the island. Like so:

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