Interesting Puzzle

ihardlyknowher · #1 07-23-2005, 03:47 AM

Forgive me if this has been posted or if it is trivially easy. I found it interesting.

Your are given 12 marbles, identical in appearance. Exactly one marble has a mass either slightly more OR slightly less than the other 11 (the difference is so minimal no human could possibly detect it without the use of scientific equipment). You are given a balance and allowed to use it exactly 3 times. You must determine which marble has a slightly different mass and whether it has more or less mass than the other 11. How do you do it?

Dov · #2 07-23-2005, 04:34 AM

This would be trivial if you knew whether it was more or less massive. Isolating it would then go as follows (assuming more massive):

1. Place 6 on each side and discard the lighter ones
2. Place 3 of the remaining 6 on each side and discard the lighter ones
3. Place 1 of the remaining 3 on each side:
A. If one side is heavier than the other, then that is the target.
B. If they both balance, then the target is the one not on the balance.

I still have to think more about modifying this procedure to answer the original problem.

Dov · #3 07-23-2005, 04:38 AM

New approach!

Roll them all down an inclined plane and the one that arrives out of phase with the others is the different one.

If it arrives earlier, then it is more massive.
If it arrives later, then it is less massive.

Rent your 3 balance trials to recoup the cost of the marbles. [img]/images/graemlins/cool.gif[/img]

Quaalude · #4 07-23-2005, 04:46 AM

[ QUOTE ]
New approach!

Roll them all down an inclined plane and the one that arrives out of phase with the others is the different one.

If it arrives earlier, then it is more massive.
If it arrives later, then it is less massive.

Rent your 3 balance trials to recoup the cost of the marbles. [img]/images/graemlins/cool.gif[/img]

[/ QUOTE ]

Nope, won't work I'm afraid. Gravity will pull all objects down at the same speed (ignoring air resistance, which will have about as close to zero effect as you can get in this case). Remember that funny little experiment that Galileo did?

Dov · #5 07-23-2005, 05:14 AM

[ QUOTE ]
Nope, won't work I'm afraid. Gravity will pull all objects down at the same speed (ignoring air resistance, which will have about as close to zero effect as you can get in this case). Remember that funny little experiment that Galileo did?

[/ QUOTE ]

I know, it was a joke. Hence the smiley.

But thanks anyway.

I hope everyone's having a good weekend.

Quaalude · #6 07-24-2005, 03:41 AM

[ QUOTE ]

I know, it was a joke. Hence the smiley.

But thanks anyway.

I hope everyone's having a good weekend.

[/ QUOTE ]

Oh, sorry. Sometimes it's hard to tell. [img]/images/graemlins/tongue.gif[/img]

lucktard · #7 07-23-2005, 05:05 AM

<font color="white"> Divide the marbles into 3 groups of four and compare the weight of two of the groups. If they weigh the same then one of the 4 unweighed marbles is the "bad" one, this is trivial to solve.

Otherwise you have 8 marbles that could possibly be bad (4 that could be light and 4 that could be heavy) and 4 marbles that you know are good. Call the 4 on the light side 1-4 and the four and the heavy side 5-8. Now compare the weight of marbles 1, 2, and 5 with the weight of marbles 3, 4, and 6.

If the scale now balances, either 7 or 8 is heavy, use the last weighing to determine which.

If side 1,2,5 is now heavy then either 3 or 4 is light or 5 is heavy. Measure 5 and 3 against two of the known good marbles. If side 5,3 is heavy, then 5 is heavy, if it's light then 3 is light and if it balances then 4 is light.

If side 3,4,6 was heavy in the second measurement then 1 or 2 is light or 6 is heavy. Weight 3 and 4 against two good marbles to find out which.
</font>

ihardlyknowher · #8 07-23-2005, 01:11 PM

Had you seen this before?

PairTheBoard · #9 07-24-2005, 06:32 PM

I like your innovation at the tricky part better than mine.

PairTheBoard

BruceZ · #10 07-23-2005, 07:07 AM

[ QUOTE ]
Forgive me if this has been posted or if it is trivially easy. I found it interesting.

Your are given 12 marbles, identical in appearance. Exactly one marble has a mass either slightly more OR slightly less than the other 11 (the difference is so minimal no human could possibly detect it without the use of scientific equipment). You are given a balance and allowed to use it exactly 3 times. You must determine which marble has a slightly different mass and whether it has more or less mass than the other 11. How do you do it?

[/ QUOTE ]

I saw a more difficult version of this problem where you are not allowed to base your measurements on the result of previous measurements. Everything else is the same.