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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