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John and Bob were doing some home construction and decided to take a beer break. Before grabbing a seat John pulls out 3 planks of wood, 1 nail and a hammer. John makes a bet with Bob saying

I'll bet you a beer you can't make a triangle given just these 3 planks and only 1 nail! As an added rule, I must be able to pick it up without it breaking what ever you did.

The nail is only long enough to attach 2 planks of wood together and each plank is of equal size and shape. No other nails or hardware can be used to attach the planks together, only the single nail.

Bob is given no extra tools besides the hammer which is for hitting the nail into any plank.

How can Bob win the bet?

Note: Murder is not allowed! (John was smart and hid his beers first!)

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    $\begingroup$ So I guess that with the "murder is not allowed" qualifier, my answer of "hammer the nail into John's head until he cries Mercy and gets you a beer" is probably not valid? $\endgroup$ – Bailey M May 14 '15 at 18:34
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    $\begingroup$ @BaileyM, Plot twist, John is a complex robot that feels no emotions or pain. It is John, who is not allowed to murder Bob! $\endgroup$ – Mark N May 14 '15 at 18:57
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    $\begingroup$ My solution: Bob refuses the bet and buys his own beer. Because really, it's just a beer, why bother? $\endgroup$ – MackTuesday May 14 '15 at 20:04
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    $\begingroup$ Coming from physics.SE, I read the title as "3 Plancks, 1 nail" xD. I guess you could present that as having to reconcile thermodynamics, quantum mechanics and electromagnetism using only one force :P $\endgroup$ – mechalynx May 14 '15 at 21:15
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    $\begingroup$ No way to answer this for certain. How would we know if the "contraption" would fall apart or not? We don't know what forces are being applied to lift it and how it will be lifted. We don't know if the wood planks were almost ready to snap before beginning "construction" of the triangle. Also, a 2nd nail could be used. The problem stated given only 1 nail but didn't state he couldn't use a 2nd nail (maybe from his own supply of nails). Basically another badly worded question is what this boils down to. $\endgroup$ – David James May 15 '15 at 1:30

13 Answers 13

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Bob could just

use the nail to scratch a triangle into one of the planks.

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    $\begingroup$ Another interesting approach. Didn't think about this one either! $\endgroup$ – Mark N May 14 '15 at 19:31
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This solution seems a bit too labor-intensive to do on a beer break, but screw that, John isn't winning this bet.

Scratch/carve out a groove (with the clawed side of the hammer) in two planks that the other plank can fit partway into. Wedge them into it and then nail the other ends together. enter image description here

This seems to me like it fits the description without any real trickery. If done correctly, it shouldn't fall apart, although this depends mostly on Bob's skill.

Source: I'm a Master Carpenter in Fantasy Life :P

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  • $\begingroup$ Who said the hammer has a "clawed" end? Many don't. $\endgroup$ – David James May 15 '15 at 1:03
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    $\begingroup$ @DavidJames Given that it isn't specified, I think it's fair to assume they're using a claw hammer (or framing hammer). It's the most common hammer sold, and the go-to tool when using nails and wooden planks for home construction, which is what they are doing. $\endgroup$ – Set Big O May 15 '15 at 1:15
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    $\begingroup$ @DavidJames and even if it isn't, you could scrape a groove via repeated application of the nail point if you were desperate enough. $\endgroup$ – Hellion May 15 '15 at 1:59
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Bob can:

hammer the nail into a triangle, ignoring the boards completely.

Or, he can

hammer the nail partway into a plank, and then whack it at an angle until it forms a triangle with the plank. With a decent initial hammering, you should be able to pick the plank up by the nail without pulling it apart.

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    $\begingroup$ Interesting approach. $\endgroup$ – Mark N May 14 '15 at 18:29
  • $\begingroup$ @MarkN, not sure if it fell within the acceptable range of "lateral thinking", but I thought I'd run with it. :-) $\endgroup$ – Hellion May 14 '15 at 18:32
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Bob could:

Nail two planks together, then squeeze the third one between them such that it goes over the bottom one and below the top. It can be picked up horizontally, or even vertically if the nail is tight and the planks are rough enough to hold their weight through friction. Here is an example using pencils. The rubber band represents the joint:

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This would be my approach:

Nail two of the planks together to form an L shape. Now, with the join pointing down, rest the third plank across the ends of the first two planks. You can't turn it upside down of course, but it certainly won't "break" by just picking it up in its original orientation.

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    $\begingroup$ I'd add to that that one could hammer the third plank into the L as the hypotenuse of the right-angled triangle with sufficient force that it all holds in place. This assumes that the nail and joint is strong enough to keep everything together, giving you a right-angled inner triangle. (This isn't very lateral thinking, but I think the best of all the answers, and gets around the lack of claw for @Geobits' answer) $\endgroup$ – Ken Y-N May 15 '15 at 1:12
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This is my answer:

Bob nails the very end of the flat side of one plank to the butt of another plank, forming a smooth "L" shape. Bob then lays this object so that the bend of the L is pointing upward. The two diagonal slopes now make a triangle with the floor and the object can be picked up without it breaking. The 3rd plank is ignored entirely.

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  • $\begingroup$ This was my intended solution! But I'll give some time in case someone else can think of other creative solutions. $\endgroup$ – Mark N May 14 '15 at 19:14
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    $\begingroup$ @MarkN How is it a triangle once it's picked up? A triangle has to have 3 sides. $\endgroup$ – pacoverflow May 14 '15 at 19:46
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    $\begingroup$ @pacoverflow I feel a little dirty that I purposely made it so it wasn't stated (that the triangle needs to remain intact when lifted), but rather only what was 'created' needed to remain intact (the "L" shape). But this was part of the puzzle. $\endgroup$ – Mark N May 14 '15 at 19:49
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    $\begingroup$ Actually this answer is wrong. In order to pick it up (the triangle), it has to remain a triangle just for split second but it wont because it will break contact with the ground. $\endgroup$ – David James May 15 '15 at 1:06
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    $\begingroup$ @MarkN (Sort of) obligatory XKCD: xkcd.com/169 $\endgroup$ – mdc32 May 15 '15 at 2:23
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This is an answer which ignores the third plank.

enter image description here

The brown rectangles are two planks, the black line is the nail. The triangle is highlighted in yellow. Basically, you place the planks with a vertex in common, then you bind them with a nail. If the nail is well inserted, the whole structure is rigid.

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    $\begingroup$ You DO know that one of the ends of a nail is the head, which is flat, right? $\endgroup$ – JLee May 15 '15 at 16:36
  • $\begingroup$ @JLee Do you know that there are three dimensions, right? Perhaps it's not clear, but my nail isn't parallel to the planks. It first perforates the top surface of one plank, then its lateral one, finally sticks in the other plank. $\endgroup$ – leoll2 May 15 '15 at 17:10
  • $\begingroup$ @leoll2 Oh ok I see now. It wasn't clear from the drawing. $\endgroup$ – JLee May 15 '15 at 17:12
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I figure this would work well enough to win a beer:

Nail two of the boards together at the ends where the red arrow is pointing. Then bend them into a L shape and lay them across the third board. With a little work and assuming the planks aren't too wide, you should have a triangle in the middle between the three. If you then pick up the whole thing where the green arrow is pointing, with a little trial and error to get the balance right, it won't fall apart.

boards

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Answer 1:

Nailed 2 pieces together as below to form a triangle shape

enter image description here

Answer 2:

since murder isn't allowed, Bob can break John's arm into a "L" shape, nailed a piece of wood into his broken arm's palm, and form a triangle. John can surely pick it up without breaking 'the wood', but I doubt Bob will win the beers this way

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    $\begingroup$ For answer 2, You can already do that without breaking his arm! So violent (but clever). Lol $\endgroup$ – Mark N May 14 '15 at 19:23
  • $\begingroup$ @MarkN Lol, I was afraid John's gonna cheat! $\endgroup$ – Alex May 14 '15 at 19:35
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Simplest solution yet.

Lay this on a plank of wood. John can pick up the plank and marvel as Bob collects his beer.

Nail and hammer

If you want to get technical about straight lines, he could flip the nail the other way, and use a plank to jam the 'head' of the nail into the hammer shaft to form a straight angle, or simply use the hammer to bend the nail head to the desired angle before producing this solution.

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  • $\begingroup$ Haha, nice. That's really a mallet though, and Bob wasn't given any mallets ;) $\endgroup$ – CactusCake May 14 '15 at 21:42
  • $\begingroup$ @JoeMalpass He may have been given a mallet, which is a type of hammer. ;) $\endgroup$ – Samthere May 15 '15 at 8:47
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I was going to suggest

scratching a triangle into the wood

but it looks like Sean beat me to it.

As an alternative to this, Bob could

'Punch out' a triangle shape with the nail.

or to reduce his work, depending on the thickness/shape of the planks he could

Score a diagonal line from one of the corners, and then break it off by standing on it and hammering the triangle off to form something like this;Triangle wood

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You can form many triangles by the following:

Stack 2, 3, or an infinite number of boards (depending on the lenth of the nail) on top of each other and drive the nail through the wood near the end. Then you can fan the boards out forming multiple triangles. See this image for the general idea. enter image description here

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  • $\begingroup$ I changed my picture to make it more obvious as to what I mean $\endgroup$ – Keltari May 15 '15 at 16:29
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"The nail is only long enough to attach 2 planks of wood together and each plank is of equal size and shape"

I imagine this doesn't mean what it literally means but rather that the nail is shorter than twice the smallest dimension of the planks.

Attach three corners of the planks with a single nail to make two corners of the triangle like this:

Solution

If the nail is good enough, one can pick it up without destroying the third corner. In practice, however, I wouldn't bet this works with real planks and nail...

(Here, the nail is used to attach 3 planks together, but in principle this can be done no matter how short the nail is compared to the plank, so I guess this isn't against the rules.)

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