Puzzle time!

[fluffymark]

Insomnia makes me do odd things. Last night I decided to twist a well known puzzle to make it more evil, and then solve it, which I did. And this stopped me thinking of monsters under the bed and other scaries (I read the Nightmares and Fairy tales graphic novel yesterday, and it may have gotten to me...ooops), so was actually a good thing, I'm trying to tell myself.

Anyway, lets see which of you clever people solves this first: (all comments initially screened)

You have a balance scale and a big bag of marbles. The marbles are all identical in weight. You take 39 of the identical marbles and mix in another special marble (so 40 marbles now), which may be heavier or lighter than the others, or may not, but looks identical, so can be identified by weight alone. Allowing only 4 weighings, how can you identify whether the special marble is heavier or lighter than the others, and if so, which marble it is?

Update: Congratulations to the clever ixwin who solved it by adding more marbles from the bag. So, lets make the problem HARDER. Assume the bag only has one more marble left in it. You have the original 40 marbles (39 identical and one special) and a bag with one more marble in it. Now solve it.

Comments

[karen2205]

Umm - how about

1, Weigh the whole bag - this gives you the weight of 39× + y.
2, Weigh an individual marble - this either gives you × or y.
3, Weigh another individual marble - again you either get × or y.

If 2 and 3 are the same weight then you know they were both ×, so multiply that weight by 39 - giving the weight of the 39 original marbles and subtract that from the total weight of the bag. The answer is the weight of y and you can tell from this whether × is greater than y.

If 2 and 3 are different weights then one is × and one is y, so weigh another marble to find out which one is which.

(am I anywhere close to the mark with this? am I missing something obvious? eg. 39 marbles identical in weight - doesn't mean they're identical in other respects.)

[fluffymark]

Ooops. No, thats way out.

Clarification: It's a balance scale. You put some marbles on one tray, some others in another tray, and it either balances or one side goes up and the other side goes down. That is all it tells you.

You also need to identify which marble is the odd marble, if it is not the same weight as the others. This is the real challenge.

The marbles are all totally identical in appearance. One marble may have a different weight. You can label them 1-40 for identification purposes.

[deborah_c]

For further clarification: are you required to work out which of "lighter" or "heavier" the odd marble is, assuming that it is one of them, or simply that it is different from the others?

[fluffymark]

Yes, you are required to find out which of "heavier" or "lighter" it is.