On a table there are three cups and one banknote (a dollar bill will do). These are the only objects you may use, with the goal of placing one of the cups, upright, above the other two, without any of the cups touching another cup. The cups must be upright at all times.

Three cups and bill drawing

There's nothing special about the bill; it will bend if you suspend it between two cups and place the third on top of it.

There are at least three very different solutions to this problem!

No lame tricks:

  • there is gravity
  • the cups are of regular weight; correct solutions can even support tumblers or shot glasses
  • the bill is a regular bill, such as a $1 bill
  • there's nothing in the cups
  • can't use any other objects or external support (e.g. holding the cup in someone's hand)
  • can't melt or otherwise dramatically alter the cups (think "glasses" instead)
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    $\begingroup$ youtube.com/watch?v=GsyKiZwTnPQ $\endgroup$ – Himanshu Sep 23 '15 at 6:34
  • $\begingroup$ If the bottom of the top cup is below the level of the tops of the bottom cups, does that still count as being "above" them? $\endgroup$ – Kevin Sep 23 '15 at 13:54
  • $\begingroup$ @Kevin: nope. All parts of the 3rd cup must be above the other two cups. $\endgroup$ – Dan Dascalescu Sep 23 '15 at 22:07
  • $\begingroup$ @Himanshu: I've accidentally upvoted your comment, thinking it was a video of the solution, but actually it's not. I can't retract my upvote. Since there's only one vote, can you please delete the comment and post it again? $\endgroup$ – Dan Dascalescu Sep 23 '15 at 22:08
  • $\begingroup$ @DanDascalescu, video shows how you can place cup on a dollar bill. as shown in picture you need to change shape of the dollar bill and remaining arrangement will be same. $\endgroup$ – Himanshu Sep 24 '15 at 4:00

You could fold the bill back and forth into a W (or maybe more folds) and use it as a rigid support.

You could push the bottom two glasses together and put the money in between the bottom glasses and the top one.

  1. You could roll the money to form a column, with the one end bent and flattened at the height of one of the other cups. Then rest the top cup on the money column with the fanned money and one of the cups for balance. No need for the second cup.

  2. You could roll it in a column and balance the top one on that. (thanks @Tim)

2a. Same as above, but with the note in one of the cups.

  1. Fold the note long wise, near one of the long edges and parallel to that edge. Wrap it around the lip of one of the cups. Put that cup in the middle of a stack. The three cups will be stacked upright, but not touching because of the note (this depends on the definition of "above").
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  • $\begingroup$ Excellent! These are all the solutions I could think of. $\endgroup$ – Dan Dascalescu Sep 23 '15 at 6:30
  • $\begingroup$ I'm trying to think of more, but I'm struggling $\endgroup$ – Dr Xorile Sep 23 '15 at 6:32
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    $\begingroup$ I could eliminate the last restriction, about altering the cups, but I think that would degenerate the problem. $\endgroup$ – Dan Dascalescu Sep 23 '15 at 6:33
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    $\begingroup$ Well, I'm not sure how 'sturdy' dollar bills are, but if it's a 'fresh' banknote, you would roll that into a roll, set it up as a column, and balance the top cup on that, without even having to rely on any of the bottom cups. Question states 'above', but not if that requires the entire cup to be above.. $\endgroup$ – Tim Couwelier Sep 23 '15 at 6:37
  • $\begingroup$ I added one more $\endgroup$ – Dr Xorile Sep 23 '15 at 6:37

Your picture already has the right arrangement:

enter image description here

(I don't have any cups on hand in the dorm, but you get the idea.)

Am I interpreting the problem wrongly, or is it just that easy? =)

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  • $\begingroup$ The part that Dan forgot to mention is that you can't move the position of the two cups in the image(the ones on top of which the third should end up). Or at least, that is how I remember this challenge $\endgroup$ – Cristian Marian Sep 23 '15 at 9:57
  • $\begingroup$ @CristianMarian: in the original puzzle, you can't move the cups. I've intentionally allowed for that in order to have a 3rd solution, as Dr. Xorile identified. $\endgroup$ – Dan Dascalescu Sep 23 '15 at 10:09
  • $\begingroup$ @DanDascalescu, being able to move the bottom cups made me think of a scenario that is „not fun at parties” and would get me a 1$ bill :). It's just as 2012rcampion's solution, but I would take the bill and put it in my pocket. This does not violate the touching rule since at an atomic level, the cups can't touch. $\endgroup$ – Cristian Marian Sep 23 '15 at 10:16
  • $\begingroup$ Wait, you have cash in a dorm room?! How times have changed... $\endgroup$ – Dr Xorile Sep 23 '15 at 16:16
  • $\begingroup$ This is what I first thought of as well. $\endgroup$ – Joe Z. Sep 24 '15 at 3:10

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