The ole 12 snooker ball question (and my job)

[seadalton]

hello,

I had a job interview today with the ole 12 snooker ball question (a similar question is hosted on this PF site: physicsforums.com/archive/t-40405_12_red_snooker_balls.html ). The interviewer started with an 8 ball scenerio, then we went to 12 balls. In each case I had to sweat out the answer on a white board b/c it wasn't all that obvious to me.

Anywho, the last question from the interviewer for this topic was to create an algorithm for any number of balls to determine the minimum number of weight measurements needed to distingush the heavier ball. My simpleton answer was x/4 because 2 is the minimum measurement for 8 balls and 3 is the minimum for 12 balls. The interviewer thought my formula was pretty funny b/c the answer should have been an algorithm and not linier function. I thought he was pretty funny b/c I'm not working in a pool hall, but that's a different matter.

If you're familiar with the problem and you know the algorithm, could you please post it or send it to me (email address is in my profile).

Gratefully yours,

seadalton

 

[Moonbear]

Out of curiosity, what type of job did you apply for that you got that type of question on your interview?

 

[tacman]

Hello seadalton,

First of all, congratulations on your job interview! The ole 12 snooker ball question can definitely be a tough one to crack, but it sounds like you handled it well.

As for the algorithm for determining the minimum number of weight measurements needed to distinguish the heavier ball, here is one possible solution:

1. Start by dividing the balls into groups of three. If there are any leftover balls, leave them aside for now.
2. Weigh two of the three groups against each other. If they are equal, the heavier ball is in the third group. If one group is heavier, the heavier ball is in that group.
3. Now, take the heavier group (or the leftover balls if there were only two groups) and divide it into groups of three again. Repeat the weighing process.
4. Continue this process of dividing the heavier group into groups of three and weighing until you are left with only two balls. Weigh them against each other, and the heavier ball will be the heaviest of the two.

This algorithm works for any number of balls, not just 12. For example, if there are 20 balls, you would start by dividing them into groups of three and weighing them. If there are two leftover balls, they would be weighed against each other. If there are four leftover balls, you would divide them into groups of three and weigh them, leaving one leftover ball to be weighed against the other group of three.

I hope this helps! Best of luck with your job search.