Balance the Balls!

[Alan McDougall]

Good morning people,

 

The 12 odd ball problem!

 

Here is a statement of the task.

 

There are twelve balls, all the same size, shape and color. All weigh the same, except that one ball is minutely different in weight, but not noticeably so in the hand. Moreover, the odd ball might be "lighter" or "heavier" than the others.

 

Your challenge was to discover the odd ball and whether it is lighter or heavier.

 

You must use a beam balance only, and you are restricted to "three weighing operations"

 

Alan

Edited July 9, 2008 by Sayonara³
removed fragment from original thread

[Mr Skeptic]

The 12 odd ball problem!

 

Here is a statement of the task.

 

There are twelve balls, all the same size, shape and color. All weigh the same, except that one ball is minutely different in weight, but not noticeably so in the hand. Moreover, the odd ball might be "lighter" or "heavier" than the others.

 

Your challenge was to discover the odd ball and whether it is lighter or heavier.

 

You must use a beam balance only, and you are restricted to "three weighing operations"

 

Alan

 

Belongs in the brain teasers forum.

 

I'll call the groups with potentially a heavy ball "heavy", those with potentially a light ball "light", and those with no odd balls "clean", and those with potentially either a heavy or a light ball "unknown"

 

Weigh 4 balls vs 4 balls. If the scale balances, these 8 balls are "clean" and 4 unknown; if it tips the other 4 are "clean", and you have 4 heavy and 4 light.

 

If you have 4 unknown, weigh 3 unknown vs 3 clean, then as appropriate either 1 unknown vs 1 clean, 1 heavy vs 1 heavy, or 1 light vs 1 light.

Otherwise, weigh 2 heavy and 2 light vs 1 heavy, 1 light, and 2 clean. Then weigh 1 heavy and 1 light vs 2 clean.

 

---

I only did that for fun. The only thing it proves is that imagination is just something we are better at than you.

[antimatter]

I only did that for fun. The only thing it proves is that imagination is just something we are better at than you.

 

Brilliant.

You are my new hero.

[Sayonara]

Belongs in the brain teasers forum.

 

The thread looked as if it could not be split because Alan mentioned the problem with his balls after his last word on the "vastness of space" thread, and the automerge feature joined the posts together.

 

Note to mods: the way to get around this is to select the merged posts and any child posts, and then choose "copy posts" from the post tools menu. Copy to a new thread in the appropriate forum. Then...

In the new thread: remove any irrelevant parts from the first post, which was the merged post in the old thread. Copy URL to paste in the old thread.

In the old thread: remove the irrelevant parts from the merged post, and delete the posts which were copied across to the new thread. Provide a link to the split thread if desired.

 

Alternatively, you can copy the split post to a new thread, and just move across any child posts when it is created. This reduces database clutter. Don't forget to leave edit/delete reasons so other staff can see what went on.

Edited July 9, 2008 by Sayonara³

[Mr Skeptic]

Oh, oh. Now my snarky comment at Alan McDougall looks silly, as does my lack of spoiler tags.

[Pangloss]

Rofl, I'm not sure what's more complicated, Alan's puzzle or Sayo's mod note.

[iNow]

I know you're just being silly, but...

 

Just copy the whole post, paste it as a new thread, then edit both the old and the new so the content aligns with where it lives.

[swansont]

I know you're just being silly, but...

 

Just copy the whole post, paste it as a new thread, then edit both the old and the new so the content aligns with where it lives.

 

I'm confused. At what point do you weigh the thread?

[iNow]

Probably best after you've split the child thread so as you don't skew your measurement with maternity weight.

[lakmilis]

Ok i just saw this but I would do it differently :

 

Weigh 6 balls on each side (you will know get a side which is heavier or lighter.. lets just assume one ball is HEAVIER.

 

discard lighter side, weigh 3 balls on each side , again discard lighter side.

 

weigh two balls of the 3.. if balanced.. last ball in hand is the heavier one else the heavier of the two on the beam is the heavier one.

Alright.. hehe.. couldnt solve it in 1 minute after all... (of course , one can't figure out if the ball is heavier or lighter from this blah)

[YT2095]

the Binary divide by 2 each turn is how I would do it also, and...

(of course , one can't figure out if the ball is heavier or lighter from this blah)

 

easily discerned from the scales, one side would be a Tiny bit lighter or heavier than the other, if you keep track of what`s where you can carry this info forwards.

[lakmilis]

the Binary divide by 2 each turn is how I would do it also, and...

 

 

easily discerned from the scales, one side would be a Tiny bit lighter or heavier than the other, if you keep track of what`s where you can carry this info forwards.

 

No YT.. we are wrong on that initial assumption.. (how would you know if one side is lighter due to a lighter odd ball, or the other side hevier due to the odd ball being heavier? )

 

It took me the time it took to type my proposal to figure it out... as i finished I realized OOOPS.. that doesn't work

[YT2095]

No YT.. we are wrong on that initial assumption.. (how would you know if one side is lighter due to a lighter odd ball, or the other side hevier due to the odd ball being heavier? )

 

I can see what you mean, doing it in 3 moves would be hard, but to know the Lighter/heavier I thought this;

 

suppose they all weigh 10g except for one that weighs 9.5.

when you make 2 groups of 6 you can see that one side it lighter by .5g OR the other side is heavier.

at This point you`re quite right, you Can`t tell.

but when you split and weigh again, you see another 5.g discrepancy, on one of the sides, which then means that the remaining balls not being weighed are the same weight, therefore the Odd ball is Lighter.

even if you didn`t know by how much (no markings on the scale) you can still see that it`s Lighter.

[lakmilis]

hmm YT.. I'mnot sure if i follow... let's see.

 

We decide to remove one of the sides (not knowing if its the one which is due toa heavier ball or a lighter one). We take 6 from one side which either were 'lighter'or ' heavier'. IF balanced, we now know we measured the wrong set and have one measurement left to do the other 6.. (so not really good).. it would just be down to luck IF we happened to choose the right 50 50 chance of hitting the assumption of heavy or light.

 

So no.. it is not really valid (although could work if one guessed right in the first place..) but it is not* solving it without chance.

[Sisyphus]

Mr Skeptic did it correctly to begin with. There's no point in measuring 6 vs. 6 because it literally gives you no information.

[Sisyphus]

Mr Skeptic did it correctly to begin with. There's no point in measuring 6 vs. 6 because it literally gives you no information.

[Royce]

This is simple:

 

Take the beam balance and put it under one end of the table to elevate one side.

 

Then line all the balls at the elevated edge and roll them all down at the same time.

 

The slower or faster one is the culprit.