Dang!!!!!!!! Sorry you're right.
That is not in the original problem though. The number of 20 minute fuses is unknown.
Just to be clear. In the original post all you know is that you know is:
You have:
1 box with 1 fuse
2 boxes with 2 fuses
The fuses in each box burn for identical times.
In one box they burn for 20min, in another for 1 hour and in the remaining one for approx 1 hour.
Other than this there is no other information required.
How to find in which box is which type of fuse?
OK - that requires just a slight modification.
Call the fuses A1, A2, B1, B2, and C1.
T=0
Light one end of A1, B1, and C1.
Light both ends of A2, B2.
The first fuse to burn up is a 20-minutes fuse. If it has no mate, it will burn up in 20 minutes. Otherwise it will burn up in 10 minutes - wait for its mate to burn up.
T=20
There are no 20-minute fuses left.
There are three scenarios, but two of them are equivalent.
Scenario 1 (there was only one 20-minute fuse):
The remaining fuses (A1, A2, B1, B2) have 40, 20 and 40+/-, 20+/- minutes left.
Extinguish one end of fuses A2 and B2.
Light the other end of fuses A1 and B1.
The mated pair that burns up at the same time are the 60-minute fuses.
Scenarios 2 and 3 (there were two 20-minute fuses):
The remaining fuses (call them A1, A2, C1, but they could be B1, B2, C1) have 40, 20 and 40+/- minutes left OR 40 and 40+/-, 20+/- minutes left.
Toss out the unmated fuse (C1).
Extinguish one end of fuse A2 (could be B2).
Light the other end of fuse A1 (could be B1).
If the pair burns up at the same time, they are the 60-minute fuses. Otherwise, C1 is the 60-minute fuse.
Yes!!!
I posted a simple fuse problem which you may find interesting
May I extend a warm welcome to you KuRmA, seldom have I seen a more impressive start. Although I missed the fun this time round, I hope you come up with a few more of this calibre. However, I very much doubt I could have matched Marks answer.
Thank you Tryagain. Mark is a really smart guy - I didn't expect him to solve the other riddle so quickly.
Ah, so you were intentionally deceitful! The title called it simple, but you knew otherwise. :wink:
I don't understand why it is so complicated. Maybe I am missing something about the fuses.
Why not light all fuses A1, A2, B1, B2 and C1 at once. The first one to finish is the 20min fuse. If another finishes with it then there are two 20min fuses. Now keep track of the remaining three or four fuses. If four remain, the two that finish together are 60min fuses; the other two are +/-60min. If three remain see if two finish together. If they do then they are 60min fuses. If the two from the same box don't finish at the same time then the unmated fuse is the 60min fuse.
This assumes that the 60+/- fuses don't finish at the same time: that they are unequal, but close to 60 minutes.
