# The 12 Ball Problem LO25321

From: Ching Peck Yen (personal) (chingpeckyen@pd.jaring.my)
Date: 09/08/00

Hi Walter,

I came across your post "The 12 Ball Problem LO9606" in
http://www.world.std.com/~lo/96.08/0801.html
It sounds interesting. Most importantly, it sounds like I can learn
some insights from the game. The discussion was in 1996.
But I just can't find your "summary of the novel ones".

[Host's Note: Well.. That was a long time ago... Here's a quote of the
relevant part of Walter Derzko's 1996 message. ..Rick]

> I'm giving the following 12 Ball Problem to my Conestoga College
> students next week. It's a warm up team-building exercise that I do
> in the first week in a course on learning strategies and a course on
>
> I think it would make a good exercise in most training and
> development workshops.
>
> The goal is not just to come up with one or more solution strategies
> but to explore and document your thinking on developing strategies
> that did and didn't work. Did your thinking proceeded to a solution
>
> I was told that this was an unsolvable problem but I came up with
> one solution strategy after about 15 minutes of doodling and three
> wrong starts. This one solution strategy lead to three ways of
> solving the problem.
>
> I suspect that there may be more.
>
> One hint - the solution came to me after an insight change.
>
> So here goes...
> =====================================================================
> The 12 Ball Problem
>
> There are twelve balls, identical in appearance, but one is either
> heavier or lighter than all the others. Using only a balance scale
> (ie two balanced pans and no weights) and using it only three times,
> isolate the odd ball and be able to say in which way it differs. Is
> it heavier or lighter than the rest ?
> ======================================================================

So, guess what! I did a trial to solve it, and hope to get yr feedback,
esp on thinking, reflection and insight gained from the game :)

Solution Steps:
1. Put 6 balls to each pans. Then remove three of them from each pan.
There leaves 3 balls on each pan. If the balance scale is not balance,
it means that the odd ball is one of the six on the balance pans.
Or else, the odd ball shall be one of the six being removed.

2. Place the six balls inclusive of the odd ball on the balance scale.
Each pan contains three. Then, remove one from each pan. Mark the ones
removed as group A. If the balance scale is not balance, take one more
from each pan, and mark the removed as group B; And the balls leaved in
balance pans are in group C. Using this way, I can identify if the odd
ball in which group.

3. Take the group with odd ball at one pan (says left side), and another
group in another pan. With that, I can determine the odd ball is lighter
or heavier than all the others. And to identify which one in left-side
balance pan is odd ball, just take one of them to exchange with one from
the right.

So, acceptable answer? Or I have been playing trick :)
Really, I find the rule of "using balance scale three times" a bit weak.

And, for the answers of the three questions you post, here you go.

1. How did I start? What was the sequence of your thinking?

At first, the 12 ball and the constraint of using balance scale three
times did puzzle me. I quickly try to narrow the problem scope using step
1, to reduce it so that the odd ball is one of the six. Then I tried to
repeat my step 1 strategy. But as there leave three in one pan. I can't
divide three balls into two groups, and hence I got to remove one by one.
Being constrained of the three times rule, I start puzzled what "three
times" actually means. I play a trick on this grey area, on step 2.

2. What roadblocks in thinking or what problem solving obstacles did you
experience?

The rule "using balance scale three times" sound weak to me. I give myself
a definition of "one time of using" is counting from putting something on
pan until it is empty - just to solve it professionally :) When I came up
step 2, I start puzzling if I should use the same tactics in step 1 and
save me one step. But, I suspect it wastes more time due to probabality,
though I didn't mathematically check the probablity and this possible
solving path. Finally I decide not to, just to make the problem area more
manageble. (In fact, the problem does not constraint solving in terms of
efficiency, right?)

3. If you came up with a correct solution strategy, what was the insight
change?

After step 2, I find an insight change. I have been using filtering to
narrow problem area. But, in step 3, I need to use back those I have
filtered to identify the odd ball and to determine if it is
lighter/heavier. (Would this reflect some strategy in dealing with people,
and team problem? I wonder :)

I solved the problem in 1 hr 44 minutes. Not bad, right? :)

I suspect too there is more solution, but my thinking is being blocked to
get another solution.

Sincerely wish to get your feedback and insight explanation. I wish to
learn from the game. Any more game? :)

Have a nice day!
PeckYen from Malaysia

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