Friday Logic Puzzle

[julian64]

12 balls, and one pair of balance scales.

One of the balls is odd. It is either heavier than the rest or lighter.

You have three seperate weighings to find which is the odd ball out of the twelve, and to be able to say whether its heavier or lighter than the rest.

[adycav]

http://www.pistonheads.com/gassing/topic.asp?h=0&a...

"I can hear the sirens coming..."

[julian64]

Sorry didn't see that.

But his answer isn't very elegant.

Mine is mathematical such that you do three weighings, always with the same balls, on the same scales for each three weighings, there is no decision making half way through like his, or multiple pathways to the answer.

Just the same three weighings each time and a look up table of answers.

[humpbackmaniac]

WooHoo someone quoted me!!!!!


I feel content.


PS answer is very complicated and needs a written explanation!

[him_over_there]

julian64 said:

Sorry didn't see that.

But his answer isn't very elegant.

Mine is mathematical such that you do three weighings, always with the same balls, on the same scales for each three weighings, there is no decision making half way through like his, or multiple pathways to the answer.

Just the same three weighings each time and a look up table of answers.

As a minimum, you need Log3(N) weighing attempts for N balls.

So for 3 balls, you need 1 weighing.
6 balls you need 2 weighings.
12 balls you need 3 weighings.
957 balls you need 7 weighings..

etc etc.

[TedMaul]

1)Weigh all 12
2) Weigh six of them
3) Weigh the remaining 6
The delta between the two latter measurements, is the delta of the odd one out.
Subtract this delta from the 1st measurement, then divide the resultant number by 12 and add the delta agan and that will give you the weight of the odd ball. Or

If the Weight of all 12 =A the weight of the first 6 = B and the weight of the latter 6 = C then the weight of the lightest ball = ((a-(b-c))/12)+(b-c) or something like that. But its Friday.