A Weighty ball problem?

[zoombini]

Now to make it worse, how do you tell if the odd one out is heavier or lighter?

[zoombini]

Supposing the first 4 are balanced.
Then the 2 ref & 2 sample are balanced.

its one of the last 2.

you weigh one ref & 1 sample, they balance, its the last one - which is it heavy or light?

I think there is some swapping from sides of the scale involved...

[danielf]

Like Metawraith said, in his E and G it is impossible to tell without a further weighing.

[altis]

Originally Posted by zoombini

Now to make it worse, how do you tell if the odd one out is heavier or lighter?

Follow my 'basic' program and you will be able to tell if it's heavier or lighter in every case except the last one. To arrive at ball H you will have had three balances so you'll need to compare it with one of the others to find out if it's heavier or lighter.

On balance, perhaps it would have been clearer if I'd labelled the stages 1, 2a, 3a, 3b, 2b, 3c and 3d instead of 1 to 7.

[zoombini]

Not according to one of the technical magazines we have at work.
Someone reckons to have figured it out but he's keping stum..

[zoombini]

I can do it in 1 weigh in.

Pick them all up, put into little bag, find the Mensa headquaters, go through "way in" & hand to them to solve it

[altis]

Lets set up some nomencleture(sp?)

test => left side heavier / balanced / right side heavier

1) start here
AB vs CD => goto 2a / goto 2b / goto 2c

2a) A or B is heavy, or, C or D is light
A vs B => A is heavy / goto 3a / B is heavy

3a) C or D is light
C vs D => D is light / uh? / C is light

2c) A or B is light, or, C or D is heavy
A vs B => B is light / goto 3b / A is light

3b) C or D is heavy
C vs D => C is heavy / uh? / D is heavy

2b) E,F,G or H is light or heavy
ABC vs EFG => goto 3c / goto 3d / goto 3e

3c) E,F or G is light
E vs F => F is light / G is light / E is light

3d) H is light or heavy
A vs H => H is light / uh? / H is heavy

3e) E,F or G is heavy
E vs F => E is heavy / G is heavy / F is heavy

All 8 balls resolved heavy or light in 3 tests.

Can I go to bed now?

[zoombini]

OK, you go to bed & I'll pass it on to the lads to see what they make of it.

[zoombini]

The written solution has arrived today. (The Engineer).

Number the balls 1 to 8.
Denote weighings W1, W2, W3.


W1 Put aside balls 7 & 8. Weigh balls 1, 2, 3 against 4, 5, 6.
If they balance, 7 or 8 is light/heavy.

W2 (a) Weigh 7 against any one of 1 to 6: this will show if 7 is heavy, light or the same.

W3 (a) If the same repeat with 8.

If 1, 2,3 is heavier than 4, 5, 6 on the first weighing then 1, 2 or 3 is heavy or 4, 5, or 6 is light.

W2 (b) Weigh 1, 2, 4 against 3, 7, 8.
If 1, 2, 4 are heavy then 1 or 2 is heavy.

W3 (b) Weigh 1 and any ball except 2. Either one will be the heavier, or, if the same, 2 is heavy.

If in W2 (b) 1,2,4 is light then either 4 is light or 3 is heavy.

W3 (c) Weigh 4 against anything but 3. If the same then 3 is heavy.

Hmm, too heavy for me, but I understand it now.

[altis]

Originally Posted by zoombini

The written solution has arrived today. (The Engineer).

Number the balls 1 to 8.
Denote weighings W1, W2, W3.


W1 Put aside balls 7 & 8. Weigh balls 1, 2, 3 against 4, 5, 6.
If they balance, 7 or 8 is light/heavy.

W2 (a) Weigh 7 against any one of 1 to 6: this will show if 7 is heavy, light or the same.

W3 (a) If the same repeat with 8.

If 1, 2,3 is heavier than 4, 5, 6 on the first weighing then 1, 2 or 3 is heavy or 4, 5, or 6 is light.

W2 (b) Weigh 1, 2, 4 against 3, 7, 8.
If 1, 2, 4 are heavy then 1 or 2 is heavy.

W3 (b) Weigh 1 and any ball except 2. Either one will be the heavier, or, if the same, 2 is heavy.

If in W2 (b) 1,2,4 is light then either 4 is light or 3 is heavy.

W3 (c) Weigh 4 against anything but 3. If the same then 3 is heavy.

Hmm, too heavy for me, but I understand it now.

Hmm... indeed - surely that's only part of it.

Yes, it resolves whether 7 is heavy or light in stage 2a, whether 8 is heavy or light in stage 3a, whether 1 or 2 is heavy in stage 3b and whether 3 is heavy or 4 is light in stage 3c.

But what about the cases when 1 is light, 2 is light, 3 is light, 4 is heavy or anything to do with balls 5 or 6?

[zoombini]

I dunno, thats the given answer in the magazine that posed the question.

I guess that you get to swap some of them about somewhere.

I think you swap 123 with 456 in step something... I'll ask the guys.

??