Logic Puzzle, Two Dollar Bills

Question

I read the following online, and I can't seem to figure it out: A bank robber is planning a heist of a high-tech bank vault. In order to exploit a weakness in the bank's security system, he needs to set off his dynamite exactly 45 seconds after triggering the banks silent alarm - If he sets it off earlier, a failsafe will kick in and electrocute him. If he sets it off later, the cops will be notified. The bank's security system will prevent him from bringing in any electronics or clocks, but he knows that it takes 1 minute for a 100 dollar bill to burn completely. He also knows that a 100 dollar bill burns at a non-uniform rate (there's more ink in the portraits). If he's able to take 2 100 dollar bills and a box of matches in to the bank with him, how can the robber time his dynamite?

Does anyone know a solution?

Asinomás · Accepted Answer · 2013-11-01T23:25:28.880

3

He starts by lighting one of them by both sides and the other by only one side. When the first dollar is done burning 30 seconds will have passed and the other dollar will have burned to one half. It is at this time that he starts to burn the other dollar by the other side. It will take an additional 15 seconds for half of the dollar to burn at this rate: giving you the 45 seconds.

Edit: to burn it on both sides at the same time you can fold it first to light both and the unfold it.

edited Nov 01 '13 at 23:25

answered Nov 01 '13 at 23:17

Asinomás

105,651

6

That's okay for the police alarm. What about the fire alarm? :) – Hagen von Eitzen Nov 01 '13 at 23:19
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Just a small comment, the other dollar need not be burned in half. However, the solutions still works as it has 30 seconds left to be burned. – Deven Ware Nov 01 '13 at 23:20
In my experience waving a wet towel above dissipates the smoke and makes it safe. @HagenvonEitzen – Asinomás Nov 01 '13 at 23:30
There is amazing complexity in the set of times you can make this way. I can't find the earlier questions about it, but I hope someone can. – Ross Millikan Nov 01 '13 at 23:41
@RossMillikan but with a larger amount of dollar bills right? – Asinomás Nov 01 '13 at 23:51
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Here is the question http://math.stackexchange.com/questions/40404/proof-of-recursive-formula-for-fusible-numbers – Ross Millikan Nov 01 '13 at 23:57

Logic Puzzle, Two Dollar Bills

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