I am going to see my family in three weeks. It is traditional for us to bring challenging brain teasers and riddles whenever we all get together. And I am out of new ideas.

I have read through several old threads here and checked out various puzzle sites, but nothing really new and tough has come up (probably because I have mined these threads before and used a lot of the good results). These family members are for the most part savvy folks who are well aware of the more familiar puzzles. So has anyone come across a good fresh brain teaser recently that I can use to vex the relatives?

In EMH, there are seven doors and two contestants. Here’s how the game always plays out. Behind one door the car, and the other six have goats. There are two contestants. Each contestant takes a turn picking two doors leaving Monty with three. Monty then reveals one of his doors. Goat. He then opens one door of each of the contestants. Goats again, of course. Monty next opens another of his doors revealing goat. Finally Monty opens one of the two contestant’s remaining doors. It is goat again and that player loses. Monty then turns to the surviving contestant and offers him/her a trade if the contestant so chooses. The contestant’s remaining unopened door for Monty’s. Should the contestant switch?

I love this puzzle. My sister and I argued it out several years ago.and I think I posted a version of it on the SDMB back then. But I do not think it has come up before ar the family gathering. Thanks! It is one of the best. Those not familiar are highly encouraged to wrestle it out.

Not a super-tough one. I came up with it myself, but it’s “obvious” enough that it was invented long beforehand.

You have a balance scale (like this). You’re presented with test samples in a 1-40 gram range in 1-gram increments. What’s the minimum set of reference weights you need so that you can always put the scale in balance when weighing one of the samples?

Progressively less vague hints (but no full solution):

Nope! You can do better.[/spoiler]You need 4… but what are the values?The solution is “exact”–you couldn’t weigh any more than 40 grams without more weights.The next spoiler is big, so don’t read it unless you’re really stuck.[spoiler]Remember that you can put reference weights on either tray.

This is a toughie. I have never seen this puzzle before. I am going to give it a little more time before I give up for the night. Seems like:

Seems like the weights should total 40. If the weights total 40, and there should be a 1g weight else how are you going to get 39? Now I have to just figure out the rest.

Fun! This is exactly the kind of thing I am looking for. Thanks Dr. Strangelove!

There’s a mile long train tunnel that passes through a mountain. There’s only a single line of tracks passing through the tunnel and it doesn’t split or curve at any point in the tunnel.

One day a train enters the one end of the tunnel at exactly noon. On the same day another train enters the other end of the tunnel, also at exactly noon. Neither train stops, slows down, or goes into reverse. But both are able to pass through the tunnel without a collision.

How did this happen?

Hint:The location of the tunnel is important.

Answer:The tunnel lies along a time zone boundary so the two ends of the tunnel are in different time zones. While the two trains both entered at what was their local noon, they passed through the tunnel an hour apart.

No. There’s no real funny business at all in the answer. It’s something that you could totally use in practice, and work just as well if the weight was 40 pounds instead.[/spoiler][spoiler]You are on the right track, though.

The solution is based on the existence of a guru who informs people that she sees one blue-eyed person.

What if there was no guru? Wouldn’t the same solution be possible?

What prevents one of the island’s inhabitants from imagining a hypothetical guru - somebody who doesn’t actually exist but who if they did exist would always make factually true statements? Everyone on the island can see that there are blue eyed people on the island. So a hypothetical guru could say that she sees a blue eyed person. And according to the solution, this information leads to the answer.

That means that everyone on the island, by knowing what the hypothetical guru could say if she existed, has enough information to figure out the answer. So the actual guru is unnecessary.

This may not be a good explanation; since the islanders can’t communicate except for the guru once then they can’t ever figure out if anyone knows their own eye color. They have no starting day to deduce what their eye color is, and they have no other way to coordinate. Once the guru speaks they can start counting the days to determine what color their eyes are, and since they are all perfect logicians they will all realize that and start counting.

But why is the guru necessary? What new information did the guru provide that everyone on the island didn’t already have? According to the logic of the solution, the islanders should be able to figure out their eye color without the guru.

You got it! There is a curious connection to computer science here: it is equivalent to the balanced ternary system. The elements are powers of 3, as you noticed. But each one can take on the multiplier -1, 0, or 1. So to get 21, you might have 271 + 9-1 + 31 + 10. The system has some fairly elegant properties.