[Guest]

Adam, Britney, Carl, and Dan went scuba diving and after spending a long time exploring an underwater cave, 3 of the friends discovered to their horror that their air tanks were running empty. Carl still had some air left - at least 10 minutes worth. They are all resting now in a small cave acting as an air pocket, so they are all able to breathe freely. However, to get out of the cave they need to swim through an underwater tunnel about 40 meters long before escaping the caves. With only one air tank left they have to swim through the tunnel at the most 2 people at the time sharing the last air supply between them while swimming. One person will then need to swim back with the air tank to enable 2 more to swim out of the cave, and so on.

The 4 friends are not equally good swimmers.

Adam is a very fast swimmer, and he is able to cover the 40 meters through the tunnel in 1 minute.

Britney can swim the distance in 2 minutes.

Carl can swim the distance in 4 minutes, and

Dan needs 8 minutes to swim the 30 meters though the tunnel.

Needless to say 2 people swimming though the tunnel can only swim at the speed of the slowest swimmer.

There is no other way out - no other type of trick to the puzzle. Just the rules laid out.

Any time spent in either end of the tunnel will be ignored. The answer uses only the time spent swimming.

Given the limited supply of air left they are naturally interested in getting everyone out of the cave as fast as possible. But how fast is that? What is the shortest possible time needed to get all 4 friends out of the cave?

/Uhre

[preflop]

does it take Dan 8 minutes to go through the entire tunnel or 3/4 of it? I assume the 30 meters on Dan's time was a mistake and it takes 8 minutes for him to go through the entire tunnel.

If so my answer is

16 minutes of swimming.

Adam & Dan - 8 min

Adam back - 1 min

Adam & Carl - 4 min

Adam back 1 min

Adam & Britney 2 min

totals 16 minutes.

if you meant 8 minutes for 30 meters for Dan - his tunnel time becomes 10 2/3 minutes so that total time would be 18 2/3 minutes.

[Guest]

Dan needs 8 minutes to swim the 30 meters though the tunnel.

/Uhre

I'm sorry about this error. This should have read:

"Dan needs 8 minutes to swim the 40 meters through the tunnel"

[Guest]

AB 2 min

A 1 min

CD 8 min

B 2 min

AB 2 min

15 minutes.

[Guest]

Adam is a very fast swimmer, and he is able to cover the 40 meters through the tunnel in 1 minute.

Britney can swim the distance in 2 minutes.

Carl can swim the distance in 4 minutes, and

Dan needs 8 minutes to swim the 30 meters though the tunnel.

What is the shortest possible time needed to get all 4 friends out of the cave?

Adam is pretty quick, and an accomplished swimmer. I'd guess he can make the 1 minute underwater holding his breath (I could, and I'm not so fit anymore).

I'd say it's

Dan+Adam = 8

Adam return = 1

Carl+Britney = 4 and Adam swims ahead of them.

13 minutes, counting on Adam's decent lung capacity.

Seems like a reasonable assumption anyway.

[Guest]

16 minutes of swimming.

Adam & Dan - 8 min

Adam back - 1 min

Adam & Carl - 4 min

Adam back 1 min

Adam & Britney 2 min

totals 16 minutes.

if you meant 8 minutes for 30 meters for Dan - his tunnel time becomes 10 2/3 minutes so that total time would be 18 2/3 minutes.

Sorry, this is the most obvious answer, but not the correct one.

AB 2 min

A 1 min

CD 8 min

B 2 min

AB 2 min

15 minutes.

This is, however, the correct answer (at least I can't see any faster solution). Well done, mate.

I can't say that I'm surprised that this was solved this quickly. I guess I'll have to try a bit harder for the next puzzle.

/Uhre

[Guest]

Adam is pretty quick, and an accomplished swimmer. I'd guess he can make the 1 minute underwater holding his breath (I could, and I'm not so fit anymore).

I'd say it's

Dan+Adam = 8

Adam return = 1

Carl+Britney = 4 and Adam swims ahead of them.

13 minutes, counting on Adam's decent lung capacity.

Seems like a reasonable assumption anyway.

Well, I cannot reject your reasoning. However, I did specifically state "There is no other way out - no other type of trick to the puzzle. Just the rules laid out.". I would consider your solution to be an "other type of trick to the puzzle"

/Uhre

[Guest]

i see what you mean.... though i still like QUOTE (LichWriter @ Apr 1 2009, 09:00 PM)

Spoiler for I think it's quicker than that...:

Adam is pretty quick, and an accomplished swimmer. I'd guess he can make the 1 minute underwater holding his breath (I could, and I'm not so fit anymore).

I'd say it's

Dan+Adam = 8

Adam return = 1

Carl+Britney = 4 and Adam swims ahead of them.

13 minutes, counting on Adam's decent lung capacity.

Seems like a reasonable assumption anyway.

Well, I cannot reject your reasoning. However, I did specifically state "There is no other way out - no other type of trick to the puzzle. Just the rules laid out.". I would consider your solution to be an "other type of trick to the puzzle"this one better

Edited April 1, 2009 by unreality_isn't_reality

[Guest]

18.7 minutes

[Prof. Templeton]

Since any solution involving Dan will require more time then they have air remaining, B or C distracts D, while A konks him on the head with an empty air tank. The remaining 3 get out in 7 minutes. Well before D wakes up. If they're feeling remorseful afterwards they can call for a rescue and an ice pack.

[Guest]

I have a different point of view.

You appear to be assuming that the minutes taken by a trip with the slower partner does not require oxygen for the faster partner. Even if no sneaky or "other" solutions are possible all swimmers (1 or 2 in these cases) have to breathe on the way which would actually slow them down from having to take time to pause for the person not wearing the tank to transfer the breather to them for long enough to take a breathe. Keeping it as close to the simple version that you are looking for here is my solution.

Air

Minutes Swimmer(s)

4 (2 x 2) Adam & Britany

1 Adam

16 (8 x 2) Carl & Dan

2 Britany

4 (2 x 2) Adam & Dan

----------------------------

27 Total

Thoughts?

Kisa

Well, I cannot reject your reasoning. However, I did specifically state "There is no other way out - no other type of trick to the puzzle. Just the rules laid out.". I would consider your solution to be an "other type of trick to the puzzle"

/Uhre

[Guest]

I think the puzzle asks what is the quickest way out. That being said Adam and Dan would swim = 8 minutes + 1 minute for adam to return, Adam would then swim with Carl which would take 4 minutes + 1 back for adam (14), then Adam would swim with Britney which would take 2 minutes making it a total of 16 minutes the quickest way to get everyone out with one tank of air.

Edited April 1, 2009 by Joshuacm214

[Guest]

I say you just send Adam out and have him get help. That way you don't have to worry about how much oxygen they have left.

Haha, but actually, 15 minutes is the least amount possible.

[Guest]

I say you just send Adam out and have him get help. That way you don't have to worry about how much oxygen they have left.

Haha, but actually, 15 minutes is the least amount possible.

How 15?

[Guest]

Joshuacm214, even though I'm quite new to this forum, I'm fairly sure that all the hiding-the-answers-behind-spoiler-buttons is done deliberately in order not to reveal the answers to anyone still trying to solve the possible.

In other words - please use the "spoiler" tag when posting possible answers to puzzles.

/Uhre

[Guest]

Sorry guys

Edited April 1, 2009 by Joshuacm214

[Guest]

I have a different point of view.

You appear to be assuming that the minutes taken by a trip with the slower partner does not require oxygen for the faster partner. Even if no sneaky or "other" solutions are possible all swimmers (1 or 2 in these cases) have to breathe on the way which would actually slow them down from having to take time to pause for the person not wearing the tank to transfer the breather to them for long enough to take a breathe. Keeping it as close to the simple version that you are looking for here is my solution.

Air

Minutes Swimmer(s)

4 (2 x 2) Adam & Britany

1 Adam

16 (8 x 2) Carl & Dan

2 Britany

4 (2 x 2) Adam & Dan

----------------------------

27 Total

Thoughts?

Kisa

Well, my thoughts are...

I should have known that in a forum like this I would lack the language skills to describe a puzzle in a way that will eliminate all attempts at picking the puzzle apart

Anyway, you have a point of course. But the whole cave-tunnel-airtank-description was all just an attempt at presenting a simple logic problem in a realistic way.

/Uhre

[Guest]

I got 15 the same way SCSW did. A and B go (2) and A comes back. (1) Then C and D go (8) and B comes back. (2) then A and B go. (2) 2+1+2+8+2 is 15.