[bonanova]

For reasons known only to yourself, you want to eat a really hard-boiled egg.

You decide that a nine-minute boil will suffice.

If only you had a timer!

As luck would have it a weird peddler happens by.

For the incredibly low price of $0.39, offers you an inexhaustible supply of 4-minute and 7-minute fuses.

The fuses are guaranteed to burn at a constant rate of speed.

You go to the kitchen and bring a pot of water to a rapid boil.

What is the shortest elapsed time before you can eat your guaranteed 9-minute egg?

Edit: see post #3.

Edited August 17, 2009 by bonanova
Change fuse to hourglass. Thanks to Gmaster.

[Guest]

Start one hourglassof 7 and one of 4 minutes simultaneously. When 4 mins are passed invert 4min hourglass immediately. when 7 minutes are passed invert 7min hourglass immediately. When 8 mins are passed invert 4min hourglass immediately. When 12 mins are passed invert 4min hourglass immediately and start boiling the egg.when 14 minutes are passed invert 7min hourglass immediately. At the end of 7 more minutes the egg will be boiled for nine minutes.

[Guest]

1. start the 4 and 7 hour glasses together.

2. Flip both when 4 is over in 4 min. glass-- 4 mins.

3. Flip both when 3 is over in 7 min. glass-- 7 mins.

4. Flip both when 1 is over in 4 min. glass-- 8 mins.

5. Flip both when 1 is over in 7 min. glass-- 9 mins.

However, it will take a minute more to remove the shell out of it..so, u can eat the egg in 10 minutes :-)

For reasons known only to yourself, you want to eat a really hard-boiled egg.

You decide that a nine-minute boil will suffice.

If only you had a timer!

As luck would have it a weird peddler happens by.

For the incredibly low price of $0.39, offers you an inexhaustible supply of 4-minute and 7-minute fuses.

The fuses are guaranteed to burn at a constant rate of speed.

You go to the kitchen and bring a pot of water to a rapid boil.

What is the shortest elapsed time before you can eat your guaranteed 9-minute egg?

Edit: see post #3.

[Guest]

OK, now what's the hourglass solution implemented by fuses?

I will make one assumption:

Assumption: You can stop fuses from burning and re-light them later in order to mimic the functionality of an hourglass.

One 7-minute fuse (A) and Three 4-minute fuses (B,C,D) are necessary

9 minute solution:

0:00 Start the 7-minute (A) and 4-minute fuse (B)

4:00 Fuse B finishes, Start remaining two 4-minute fuses (C, D)

7:00 Fuse A finishes, Stop Fuse D (1 minute remaining)

8:00 Fuse C finishes, restart Fuse D

9:00 Fuse D finishes.

This solution works regardless of:

In addition, the puzzle doesn't say (while it implies such) that all 4 minute fuses are the same length. In other words, you could have 5 four minute fuses, each with different burn rates and of lengths sufficient to give you exactly 4 minute burns.

I've been treating the fuses as either a 4 minute or 7 minute "black box". I.e. You press a button on the box and either 4 minutes or 7 minutes later (depending on the box; you know which is which), it "dings." However, I've been treating them as if you can't see the workings, so the only thing you know is the instant you press the button and the instant the ding occurs.

[bonanova]

I will make one assumption:

Assumption: You can stop fuses from burning and re-light them later in order to mimic the functionality of an hourglass.

One 7-minute fuse (A) and Three 4-minute fuses (B,C,D) are necessary

9 minute solution:

0:00 Start the 7-minute (A) and 4-minute fuse (B)

4:00 Fuse B finishes, Start remaining two 4-minute fuses (C, D)

7:00 Fuse A finishes, Stop Fuse D (1 minute remaining)

8:00 Fuse C finishes, restart Fuse D

9:00 Fuse D finishes.

This solution works regardless of:

That works.

Can we do it without extinguishing a fuse? Some types are difficult to stop.

[Guest]

As per the question it is 16 + 9 = 25 minutes!

[Guest]

It is 16 + 9 = 25 minutes!

[Guest]

has a nine-minute hourglass solution.

The OP uses the word form guarantee twice: once for the uniform fuse burn, once for the boil time.

Within those stated parameters, the boil time only has to be as certain as the rate of burn of the fuses.

Given that, and AT's solution [and arbitrarily ruling out lighting any one fuse in two places]

is there a nine-minute fuse solution? Specifically, can fuses emulate AT's solution?

Burn a fuse of seven minutes. when it finishes burn a four minute fuse from the middle. Another possibility is to allign two four minute fuses together and burn them from opposite sides after the seven minute fuse. when the flames pass each other it is nine minutes

[bonanova]

Burn a fuse of seven minutes. when it finishes burn a four minute fuse from the middle. Another possibility is to allign two four minute fuses together and burn them from opposite sides after the seven minute fuse. when the flames pass each other it is nine minutes

Yup, the first of those is in my post 26.

We need both assumptions about equal lengths and constant burn rates for this.

In the hourglass solution, the 7-minute hourglass has poured for 1 minute after the 4-minute glass has poured twice.

We turn the 7-minute glass over at that point and re-live its 1 minute of sand.

To do this with fuses, we need two 4-minute and three 7-minute fuses.

We light a 4 and a 7.

We lay the other two 7's side by side, ends aligned.

When the 4 has burned, we light another 4.

When the 7 has burned, we light one of the other two 7's

When the second 4 has burned, the second 7 is at the 1-minute mark.

We now simply touch the two 7's together.

The final 7 has a nice 1-minute burn, backwards to the short end, emulating the final turn of the hourglass.

[Guest]

Adaptation of my answer in post #9 but lighting only one four minute fuse for a 9 minute egg in 9 minutes:

Place the one seven minute fuse in the water with the eggs and mark the level of the water on the fuse as boiling commences (no need to light it), whilst at the same time, lighting a 4 minute fuse. After 4 minutes, remove the seven minute fuse from the water. Calculate, using finger widths, how much water has evaporated from the pan in the first four minutes (by measuring between the initial water level mark and the new water level mark on the 7 minute fuse). All things remaining equal, the water should evaporate at the same rate, so you'll then be able to calculate the where the water level on the seven minute fuse will be after 9 minutes. Mark this using a finger nail indent on the seven minute fuse. Pop the 7 minute fuse back in the water and wait for the water to reach that level. Dry out the seven minute fuse and you may be able to use it again

)

Total 9 minutes