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Fri 17 Dec, 2004 07:18 pm
We have two pieces of cord. If we put one of their ends on fire, the
first cord takes exactly 10 minutes to burn while the second takes 8
minutes. The cords are very badly hand manufactured so that there is no guarantee that the burning rate is constant throughout the cord length; if we cut the first cord in half, there's no guarantee each half takes 5 minutes to burn. You may only burn the ends, and no cutting is allowed.
Using just these two pieces of cord and a lighter, what times can you measure?
first time you can measure is:
8m short cord (lit on one end)
*========
Whim
4: light both ends of the 8 minute cord
5: both ends of the 10 minute cord
8: one end of the 8
9: both ends of 8, then both ends of 10
10: one end of 10
13: one end of 8, then both ends of 10
14: one end of 10, then both ends of 8
18: one end of 8, then one end of 10
If you don't have to be able to control when the measuring starts, you can subtract to get:
1: light both ends of 8 and 10, start measuring when 8 burns out
2: one end of 8 and 10, start measuring when 8 burns out
3: one end of 8 and both ends of 10, start measuring when 10 burns out
6: one end of 10 and both ends of 8, start measuring when 8 burns out
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