Eive Impossible Questions

[PennLady]

How big is an ice rink ?

If you're talking ice hockey, there are different dimensions in Europe and North America. European teams play on larger ice rinks.

Also although I'm sure there are rules about how deep ice has to be, as well as the hardness, I'm not sure every rink is the same.

So I guess the answer to this is going to be how you measure it as opposed to a number.

 

[Handley_Page]

If you're talking ice hockey, there are different dimensions in Europe and North America. European teams play on larger ice rinks.

Also although I'm sure there are rules about how deep ice has to be, as well as the hardness, I'm not sure every rink is the same.

So I guess the answer to this is going to be how you measure it as opposed to a number.

[Very] rough (back of a fag packet) calculations reveal that the ice in an ice rink weighs in at about 47000 Kg. I've assumed 200ft by 100ft.
You'll have to work out what that it is your local tons!

 

[PennLady]

International (IIHF) rink dimensions are 200ft x 100ft (61m x 31.5m).

An NHL rink is 200ft x 85ft (61m x 26m).

So your guess sounds good to me for the IIHF rinks, but obviously the NHL would be slightly less. Good work.

 

[Bramblethorn]

Here's another one then:

You have two identical glass balls. Dropped from a certain height (or above), they will always shatter; dropped from anything lower, they will survive undamaged.

You have a 36-floor building. You want to know what the maximum drop is that these balls can survive, to the nearest floor (it's possible that the answer is "less than 1 floor" or "more than 36 floors"). It doesn't matter if they both get smashed in the process, but obviously once you break both you can't do any more tests.

One way to do this would be to go to the first floor, drop a ball, retrieve it, then try from the second floor, then from the third, and so on, until a ball shatters. This could give you the answer in just one trial, but it might take as many as 36 trials (each drop = 1 trial).

What is the smallest number of trials in which you can guarantee finding the answer, to the nearest floor?

It's possible to do this in just 8 trials max.

First ball: go up to the 8th floor and drop the ball. Then if it hasn't yet broken, go up another 7 to the 15th and drop it again, then another 6 to the 21st and drop it again, then 5 to the 26th, 4 to the 30th, 3 to the 33rd, 2 to the 35th, and 1 to to 36th.

Once the first ball breaks, go back to the last floor tested that didn't break it, and work your way up one floor at a time with the second ball (so if ball #1 was OK on the 15th floor but broke on the 21st, try 16, 17, ... until it breaks or you get back to the floor that broke #1).

Under this strategy, if ball #1 breaks on the first trial, you need at most another 7 trials with #2 to confirm exactly where the break-point is; if it breaks on the second, you need another 6 max, and so on. So no matter where the break-point is, it ends up taking no more than 8 trials.

 

[Bramblethorn]

Another one, then:

Take an 8 x 8 chessboard and paint all the squares black. You're then allowed to take any three squares that form a 3x1 rectangle and reverse all their colours (black->white, white->black); you can repeat this as often as you like.

Is it ever possible to end up with an all-white board, and can you prove your answer?

 

[LaRascasse]

Another one, then:

Take an 8 x 8 chessboard and paint all the squares black. You're then allowed to take any three squares that form a 3x1 rectangle and reverse all their colours (black->white, white->black); you can repeat this as often as you like.

Is it ever possible to end up with an all-white board, and can you prove your answer?

Thinking out loud here...

I don't suppose it is possible. Eventually with 3X1 squares, you would end up re-colouring white squares as black.

 

[Over_Red]

That doesn't work, because this time around you don't know whether the odd ball out is lighter or heavier - so if the first two groups of 6 aren't equal, you don't immediately know which one to eliminate.

Aww, you're right. Fiddlesticks.