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

[the-alchemist.livejournal.com]

OK, this seems obvious to me. Tell me what I'm doing wrong! *wince*

WEIGHING 1
You put twenty marbles in each side. If the scale doesn't balance then the special marble is either heavier or lighter than the others.

WEIGHING 2
You lay marbles 1-20 aside.
You put marbles 21-30 in one side of the balance
You put marbles 31-40 in the other side.
If they balance, then go to 'weighing 3a'. If they don't, go to 'weighing 3b'.

WEIGHING 3a
Discard marbles 21-30 altogether and put marbles 1-10 in their place.
If marbles 1-10 weigh more than marbles 31-40, then the special marble is heavier.
If marbles 1-10 weigh less than marbles 31-40, then the special marble is lighter.
If they weigh the same, go to 'weighing 4a'

WEIGHING 3b
Lay marbles 31-40 aside.
Put marbles 1-10 in their place.
If marbles 21-30 are heavier than marbles 1-10 then the special marble is heavier.
If marbles 21-30 are lighter than marbles 1-10 then the special marble is lighter.
If they weigh the same, go on to weighing 4b.

WEIGHING 4a
Discard marbles 1-10, and repeat 'weighing 3a' using marbles 11-20 instead of them.
If marbles 11-20 weigh more than marbles 31-40, then the special marble is heavier.
If marbles 11-20 weigh less than marbles 31-40, then the special marble is lighter.
If they weigh the same then something has gone wrong!

WEIGHING 4b
Discard marbles 1-10, and repeat 'weighing 3b' using marbles 11-20 instead of them.
If marbles 11-20 weigh more than marbles 31-40, then the special marble is lighter.
If marbles 11-20 weigh less than marbles 31-40, then the special marble is heavier.
If they weigh the same then something has gone wrong!


Couldn't it be done in three weighings, leaving off weighing one? I'm sure I'm missing something here (and if I'm right, I bet there's a less long-winded way of expressing it.)

[fluffymark]

The key problem is to identify *which* of the 40 marbles it is, not just whether is is heavier or lighter. ;)

[the-alchemist.livejournal.com]

I still think I win. My superior English-studenty sentence-parsing skills cut through the Gordian Knot of your mathematical cunning.

[fluffymark]

The question was never ambiguous. Look at it. It says marble. It is your memory of an ambiguous question that is incorrect. ;)

(Orwell taught me everything I need to know...)