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ID: 163 Title: A Dutch Puzzle Replis: 3 Read: 1536 Author: 4
Name: Tom Yang  Posts: 110    Vancouver Time: 2004-5-30_1:19:18 Quote    Reply
Hugh, the Dutch sailor here, gave me a puzzle more than a year ago (no kidding) and I thought about it for a couple of hours before I gave up. I recalled it again tonight and solved the Dutch puzzle:

There are 12 billiard balls all with the same color and same size. One of them differs from the others only by a small amount of weight. For example, eleven balls each weights 300g exact but this guy weights either 305g or 295g. Now, you're given a simple balance and allowed to measure 3 times. You could compare 5 balls to 5 balls, 4 balls to 4 balls, etc.
By the end of your 3rd measurement, you have to tell me:(1) which ball is the "different" one? (2) is it heavier or is it lighter than others?

Name:  Posts:  **  Vancouver Time: 2005-1-8_19:43:4 Quote    Reply
Never trust the Dutch. Apparently there billiard ball manufacturing has a quality problem.
Name: Chetan  Posts: 8  **  Vancouver Time: 2005-2-10_1:56:0 Quote    Reply
hi all..... my first post on the forum....

hope it redeems my obvious greenhorn status

divide the balls into 3 lots of 4 each, called them ABC for convenience

Weigh A and B

They are the same weight

The ball is in lot C

Weigh A and C

That tells you if the ball is heavier or lighter

2 weighings over and you know that if the ball is lighter or heavier

You now only need to choose it from the 4 in that lot

Right so far?

If A and B were not the same weight

then weigh the heavier one (say A) against C

if A is still heavier, then obviously B and C are the same weight

so the ball is HEAVIER AND IN LOT A

If A is the same weight when you weight it against C,

then the ball is LIGHTER and is in LOT B

so this way also 2 weighings and you know

if the ball is heavier or lighter

and you know the four balls that contain the culprit



waiting to hear from y'all


Name: Jstack  Posts: 1  **  Vancouver Time: 2005-10-24_15:4:30 Quote    Reply
Solved it... Solo sailor from Chicago has time on his hands. Seperate the 12 balls into 3 groups of 4. The "simple balance" is a balance beam scale, not a scale you stand on. 1. Put 4 balls aside for right now. 2. Put four balls on one arm of the scale & four on the other. If the scale "tips" then you have the odd one on the scale (toss the four on the side away). If the scale does not "tip" toss the eight on the scale away. Go ahead and solve it from here, you only ate up "ONE" measurement. From here it is easy.