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

[fluffymormegil.livejournal.com]

Thirteen, against thirteen from the bag, gives either a pool of thirteen to chop, or a pool of 27, and reveals the direction.
If the thirteen are out of balance, weigh six against six; if they match, the thirteenth is the ringer, otherwise split the six with the ringer 3/3 and then match two of the three with the ringer.
If the 27 are out, weigh nine against nine; weigh three against three from whichever of the three nines is the ringer; weigh two of the three with the ringer.
(and I don't think your wrinkle is evil, I think it's obnoxious.)

[fluffymark]

Not quite, but close. What happens if your first weighing is balanced? You then have 27 untested marbles, and no clue about direction. All bad.