Axiom Home Page Forums General Discussion The Water Cooler Use your brain!

No, that's not an insult. I thought some people here might like a place that challenges the brain in a different way. So this will be the riddle / brain teaser thread. (This may flop completely, but it's worth a try. I know at least I love riddles. )

I'll start it off with one of my favorites.

You have 12 similar looking balls. 11 of them weight the same. One of them is slightly heavier than the others. You also have a scale. You can put balls on both sides of the scale and it'll tell you which side is heavier or will stay in the middle if both sides weight the same. Here's the kicker: You can only use the scale 3 times. How can you find the one ball that is heavier?

Put 6 balls on each side. One side will be heavier.

Take the 6 balls from the heavier side, split them into 3 each, and put them on different sides. One side will be heavier.

With the 3 balls from the heaiver side remaining, take TWO, put 1 on each side. If one side/ball is heavier, then that's the one. If they both weigh the same, then the third ball is the heavier one.



Give me another one, I'm bored at work

You can also start with 5 balls on each side, leaving 2 aside to measure if the others weigh the same.

Ok then. Here's the same riddle with a nasty twist:

You have 12 similar looking balls. 11 of them weigh the same. One of them has a slightly different weight, BUT you don't know whether it is heavier or lighter. You also have a scale. You can put balls on both sides of the scale and it'll tell you which side is heavier or will stay in the middle if both sides weight the same. Again, you can use the scale only three times. How can you find out whether the different ball is lighter or heavier and which one it is?

(I haven't been able to figure this one out, but it is solvable as far as I know.)

Umm... I give up on the second version!!! Are you sure it's solvable?


Okay, here is my favorite:

There are two rooms next to each other: one with three switches, the other with three light bulbs. Each one of these switches turns on/off one corresponding light bulb in the other room. You can come in to each room only once, manipulating/observing the switches and light bulbs. How do you determine which switch is connected to which light bulb?

I know that one Sushi, but I'll give someone else a chance to think about it for a while first.

I,m so glad to see you boys playing so nicely!

This is a nice spot for puzzles, but the best place to go is:
http://www.lateralpuzzles.com/

-Andy

Sorry about that last post, but I could not resist.
All in good fun. Please don't ban me. ;-)

Oh, and the answer to the puzzle is:
Turn switch 1 on and leave it on for 10 minutes or so.
Turn off switch 1, turn on switch 2, then go to the other room.
The light that is on goes with switch 2, the light that is off but warm goes with switch 1, and the light that is off and cold goes with switch 3.

Yes, Andy the BAD BOY, you will be evicted!!!

Now you got me thinking of a riddle I saw on a website a while ago, and could not figure out:

I have two dozen doors that lead to nowhere.

answer?

any guesses?

The Winchester Mystery House?

Doors themselves never lead anywhere; doorways do.

Blimey, I'm stumped (Doesn't take much anyways ...)

You've got a solution to this one? Or does someone just says there is one? I imagine you separate the balls into 3 groups and you have to mix and match them for the 2nd and 3rd weighings but can't get the math to work ....

I have the solution! (Ok, so I found it. ) Lemme know when you want it.

The secret lies in assigning each ball a unique "code" made up of the 3 positions that it can occupy during each use of the scale: left, right, or set aside.

Yeah, I did that -- 3 groups each (A, B, C) and each ball is numbered (A1, A2 .... C3, C4).

You weigh 2 groups first and leave one group off, then the second time you mix and match all 12 balls (hence the numbering). Right? Well at least I'm on the right track, right ...

Here's a new one, I'm not sure if it's solvable...if it is I've never been able to figure it out. Take a piece of paper and draw 3 houses (a square with a triangle on top of it). Then put the letters G, O, and W on the paper. These stand for Gas, Oil, and Water. Draw a line from the gas to each house, oil to each, and water to each. The catch is, the lines from different sources cannot cross each other. I'd post a picture but don't have a web server to do it from. I'd love to know the solution if anyone can figure it out and post a picture of the solution, or a proof that it can't be solved if it can't.

The only criteria is that you can not cross different sources. Gas is crossing itself.

That's the closest I have come. I'm looking for a way to do it where you can't run lines through the houses like you did with Gas.

Oil?

Put the gas line in the middle house then if you dont want it to go through all of them.

If gas starts in the middle it can get to 2 of the 3.

Yup, some houses out East use oil for their furnaces.

Oil-fired furnaces I'm familiar with. An oil line to the house I'm not. Even if there is such a thing as an oil line to a house, I'd expect oil lines and gas lines to be mutually exclusive.

I concur with Jason. So that leaves us with water. Water doesnt have to be mutually exclusive. Such as water in an apartment is all daisy chained from the source. So you could be getting your tap of the water through your neighbor. So in my drawing exchange the G for W and in reality should be workable.

Workable, but perhaps not what the riddler intended.

The 3 houses, 3 utilities rule has no solution. After trying endless combinations of lines on paper, I caved. I looked at some math website and turns out it is mathematically impossible. I'm not so dumb after all!

I didn't think it was solvable. If you have a link to the math website that proved it though I'd like to see it...please post it here. I won't have to feel dumb anymore either!

Here's a link with some gory details on the unsolvability of the 3 houses riddle:

http://rec-puzzles.org/new/sol.pl/geometry/K3,3

Alright, so the gory details are a bit more Geometry and proofs then I have had to think about in a while, but I think I got the general gist from that without getting into the details too much. Some of the details are a bit beyond me anyway. Thanks for the info though. I've always wondered about that one!