Puzzle: Twelve Billiard Balls

JanT · 13 Dec 2007, 18:49

In Psychology today, we were given Piaget's Twelve Billiard Balls puzzle to sort out. Why? Ask me another. Surely this would be a Maths problem.

The Twelve Billiard Balls Puzzle

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

Your challenge is 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.

Solution here.

R. · 13 Dec 2007, 20:35

Cpl Mickey · 14 Dec 2007, 18:44

Quote:

Originally Posted by R.

I'll go along with that thought R

Lord Kagan · 14 Dec 2007, 18:48

surely an easier way would be to counter balance each ball on the beam balance and whatever one isnt balanced contains the heavier/lighter ball by process of elimination?

Cpl Mickey · 14 Dec 2007, 18:54

Quote:

Originally Posted by Lord Kagan

surely an easier way would be to counter balance each ball on the beam balance and whatever one isnt balanced contains the heavier/lighter ball by process of elimination?

That sounds too easy. lol !

samurai7 · 14 Dec 2007, 19:32

Quote:

Originally Posted by Lord Kagan

surely an easier way would be to counter balance each ball on the beam balance and whatever one isnt balanced contains the heavier/lighter ball by process of elimination?

yeah, but you're only allowed three weighing processes, and there are twelve balls, innit?

duke knooby · 14 Dec 2007, 19:45

1st attempt.. 6 on each side
2nd attempt.. 3 on each side
3rd attempt.. 1 on each side.. if balanced the un used ball is the odd one.

only re weigh the heavy side

*AndyK* · 14 Dec 2007, 19:55

Quote:

Originally Posted by duke knooby

1st attempt.. 6 on each side
2nd attempt.. 3 on each side
3rd attempt.. 1 on each side.. if balanced the un used ball is the odd one.

only re weigh the heavy side

What happens if the ball that is a different weight is lighter than the other 11?

duke knooby · 14 Dec 2007, 20:04

good point...

mszee · 14 Dec 2007, 21:13

Yeah, ok...I knew that one before...started reading from the link and remembered why I forgot it...

Well, I think lesson well learned here is that it's much worse without any balls...I think so anyway...

Lord Kagan · 15 Dec 2007, 13:29

ill work my way out later... cant be fecked now

13 Dec 2007, 18:49	#1
JanT Mega Loafer Join Date: 22.06.2006 Location: Blackpool Posts: 2,232	Puzzle: Twelve Billiard Balls In Psychology today, we were given Piaget's Twelve Billiard Balls puzzle to sort out. Why? Ask me another. Surely this would be a Maths problem. The Twelve Billiard Balls Puzzle There are twelve billiard balls, all the same size, shape and colour. All weigh exactly the same, except that one ball is slightly different in weight, but not noticeably so in the hand. Moreover, the odd ball might be lighter or heavier than the others. Your challenge is 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. Solution here.

14 Dec 2007, 19:45	#7
duke knooby Mega Loafer Join Date: 24.06.2005 Location: belfast Posts: 17,888	1st attempt.. 6 on each side 2nd attempt.. 3 on each side 3rd attempt.. 1 on each side.. if balanced the un used ball is the odd one. only re weigh the heavy side Last edited by duke knooby; 14 Dec 2007 at 19:50.

13 Dec 2007, 20:35	#2
R. You dig. Join Date: 02.04.2002 Location: On the fothermucker Posts: 7,179

14 Dec 2007, 18:48	#4
Lord Kagan On the other hand, You have different fingers Join Date: 17.05.2006 Location: Belfast Posts: 8,833	surely an easier way would be to counter balance each ball on the beam balance and whatever one isnt balanced contains the heavier/lighter ball by process of elimination?

14 Dec 2007, 20:04	#9
duke knooby Mega Loafer Join Date: 24.06.2005 Location: belfast Posts: 17,888	good point...

14 Dec 2007, 21:13	#10
mszee Mega Loafer Join Date: 28.03.2006 Location: And you think you're down under??? Posts: 26,252	Yeah, ok...I knew that one before...started reading from the link and remembered why I forgot it... Well, I think lesson well learned here is that it's much worse without any balls...I think so anyway...

15 Dec 2007, 13:29	#11
Lord Kagan On the other hand, You have different fingers Join Date: 17.05.2006 Location: Belfast Posts: 8,833	ill work my way out later... cant be fecked now