Tube/Levers Puzzle

[albionmoonlight]

Here is a puzzle that I got from this board back in the day. Props to whoever introduced it in the first place; it remains one of my favorites. There are probably enough new people on the board to throw it back out here.

You are in a room that contains a floor to ceiling hollow tube. The tube contains four chest level holes placed at the points of the compass (i.e. two sets of two holes directly across from each other).

Inside of this tube is a cylinder with four levers that correspond to the four holes in the tube. Each of these levers can either be up or down. You cannot see inside of the tube, so the only way that you can tell if a lever is up or down is by putting your hand in the hole.

You can only put two hands into the tube at a time. You can either put your hands into holes directly across from each other, or in holes next to each other. When your hands are in the hole you can grab the levers and move them up or down, as your fancy takes you.

The catch is that once you remove your hands from the tube, the cylinder spins rapidly, stopping in a random place. You cannot tell where it stopped. In other words, you can put your hands into two holes and manipulate levers; however, when you remove your hands, the levers will rotate position in a way unknown to you. Up levers will stay up, and down levers will stay down, however. You cannot leave anything on a lever to mark it or anything.

Your goal is to place the levers either all up or all down. As soon as you accomplish this, you will know about it (bells, whistles, etc.).

How would you go about doing this (or--prove that it is impossible).

[albionmoonlight]

One bump. Does the puzzle make sense as written, or is it too hard to picture?

[Vince]

I can see it...however, is there a set position for the levers to start in?

My guess would be to first put your hands in opposite holes, and switch them both in the same direction...for the sake of argument, let's say up.

Then, after it rotates, put your hands in adjacent holes...that way you are guaranteed to have at least one lever that you didn't have before. Switch that one up, if necessary.

From there, I don't know a clear-cut way to get the final lever, if necessary, but if it is still necessary, you know that it's the only lever still 'down.'

[Huckleberry]

Well, I understand that you're looking for a systematic approach. But after 3 are down, odds are that after a couple of spins you'll finally get your hands on the last one. So I don't see how you can prove it's impossible to get them all up or all down. You'll eventually get it done.

I got as far as the previous poster on the approach.

[albionmoonlight]

That is the proper step one and two.

You are then in a position where you know that the levers are u,u,u,d.

Here's a hint: It can be done, and in a way that does not require you to wait for the proper spin.

[albionmoonlight]

Here is another hint--it can be done in 5 steps.

[Huckleberry]

Okay, so they're u,u,u,d

Put your hands back in opposite sides and assuming you didn't get lucky and find the down one, move one of them to down. So now they're

u,u,d,d in some configuration

Now put them back in in adjacent holes. You either have u,u in your hands or d,d. Either way, flip them.

Done.

edit - Ah crap. I guess you could have u,d or d,u of course. Well, the end of the work day nears.

[Maple Leafs]

Bump?

[albionmoonlight]

Hint--

Y'all have gotten this far.

Step 1--put hands ACROSS and flip up

Step 2--Put hands ADJECENT and flip up lever that is not up. Now you know that you have u,u,u,d

Step 3--ACROSS. If you hit d, then flip it up to win. If you hit u,u, flip one of them d to get u,u,d,d

What next?

[Maple Leafs]

I'll take a shot.

Step 4 - Adjacent: if you hit UU or DD, flip both an win. If you hit UD, flip both to create UDUD

Step 5 - Across: flip both to win.

Yes?

[albionmoonlight]

Originally posted by Maple Leafs
I'll take a shot.

Step 4 - Adjacent: if you hit UU or DD, flip both an win. If you hit UD, flip both to create UDUD

Step 5 - Across: flip both to win.

Yes?

Yes.

This is one of those puzzles that, even after I learned the answer, still had trouble remembering. And, when I first read it, I would have bet big $$$ that it was impossible.

Good job, all.

[KWhit]

The thing that got me was that I kept overlooking the fact that they could be all Up or all Down.