Robbie is building another engine…

[telford dorr]

Had trouble sleeping last night due to an annoying head cold. Figured that thinking about this piston problem would have to put me to sleep. So I did. It didn't work.

First, the concept of having 12 equally balanced OG pistons available was a bit overwhelming. But wait, there's only 11. One is off a little. Gotta fix that.

We know, from the way the problem was worded, that the correct answer is 3 weighings. But how? So try this:

For the sake of discussion, number all of the pistons with a black Sharpie 1 through 12. Label the scale pans A and B.

1) Put pistons 1-4 on pan A and pistons 5-8 on pan B. Leave pistons 9-12 on the bench. Note the balance. There are 3 possibilities:

1a) The scales balance.
1b) Pan A is heavy
1c) Pan B is heavy.

(1a) Suppose the pans balance. We know the bad piston is in group 9-12 still on the bench, and that pistons 1-8 are all good. Put them to the side of the bench. Now put piston 9 on pan A, along with 1 of the good pistons. Put pistons 10 and 11 on pan B. Note the balance. Again, there are 3 possibilities:

2a) The scales balance
2b) pan A is heavy
2c) Pan B is heavy

(2a) If the pans balance, then we know that piston 12, still on the bench, must be the bad piston. Comparing it to any of the good pistons will determine if it is heavy or light.

(2b) If pan A is heavy, then either piston 9 is heavy, or either piston 10 or 11 is light. Put piston 10 on pan A and 11 on pan B, and note the balance. 3 possibilities:

3a) The scales balance. Piston 9 must be heavy.
3b) Pan A is heavy. Piston 11 must be light.
3c) Pan B is heavy. Piston 10 must be light.

Done.

(2c) Pan B is heavy. Same as (2b), (3a-c) above, but the bad piston has the opposite weight offset.

Done.
Otherwise, back to the first 8 pistons.

(1b) Pan A is heavy.
(1c) Pan B is heavy.

We know that pistons 9-12 are all good.

Put pistons 6, 7 and 8 on the bench.
Leave pistons 1 on pan A. Move pistons 2 , 3 and 4 from pan A to B. Add 3 good pistons to pan A. So, the setup looks like this:
Pan A = piston 1 and 3 good pistons
Pan B = pistons 5, 2, 3 and 4. Note the balance. 3 Possibilities:

2d) The scales balance. If coming from path (1b), this means that one of pistons 6, 7 or 8 is light. Compare pistons 7 and 8. If they balance, it's piston 6 that is light. Otherwise, it's the lighter of 7 or 8 that's bad. If coming from path (1c), the bad piston will be heavy instead of light.

2e) Pan A is heavy, and pan A in weighing 1 was also heavy, or pan B is heavy, and Pan B in weighing 1 was also heavy: Because pistons 2, 3, and 4 swapped sides, but the balance didn't change, then either piston 1 is bad or piston 5 is bad. Compare piston 1 to a good piston. If they balance, then piston 5 is bad, otherwise piston 1 is bad. If from path (1b) if it's piston 1 then it's heavy, or piston 5 is light. If from path (1c), then it's the opposite.

2f) Pan B is heavy, and was light in weighing 1, or pan B is light, and was heavy in weighing 1:. if coming from path (1b), one of pistons 2, 3, or 4 is heavy. If from path (1c) then 2, 3 or 4 is light. Compare pistons 2 and 3. If they balance, it's piston 4 that's bad. Otherwise, it's pistons 2 or 3. If coming from path (1b), the bad piston is heavy. If from path (1c), it's light.

Done.

Because I came up with a solution (I think...), I obviously didn't sleep. Now I feel like crap.
_________________
'71 panel, now with FI
'Experience' is the ability to recognize a mistake when you're making it again - Franklin P. Jones
In theory, theory works in practice; in practice, it doesn't - William T. Harbaugh
When you're dead, you don't know you're dead. The pain is only felt by others.
Same thing happens when you're stupid. - Philippe Geluck
More VW electrical at http://telforddorr.com/ (available 9am to 9pm PST)

[Abscate]

Why are you here, Telford?


_________________
.ssS!

[telford dorr]

I don't know. Ask me again after I've had some sleep...
_________________
'71 panel, now with FI
'Experience' is the ability to recognize a mistake when you're making it again - Franklin P. Jones
In theory, theory works in practice; in practice, it doesn't - William T. Harbaugh
When you're dead, you don't know you're dead. The pain is only felt by others.
Same thing happens when you're stupid. - Philippe Geluck
More VW electrical at http://telforddorr.com/ (available 9am to 9pm PST)

[Brian]

_________________
Wash your hands

'69 Bug
'68 Baja Truck
'71 Bug
'68 Camper

Only losers litter

[cdennisg]

Just read through the entire thread. My brain hurts.
_________________
nothing

[notchboy]

[wcfvw69]

[airschooled]

[heimlich]

I'm still waiting on the engine to be built.
_________________
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[richparker]

[airschooled]

[Brian]

Get the Web 110/163 and you can use my Spanish IDFs.
_________________
Wash your hands

'69 Bug
'68 Baja Truck
'71 Bug
'68 Camper

Only losers litter

[wcfvw69]

[Clatter]

I just tried to solve the scale thing,
And only one piston would fit into each of the little pans.

So you're all wrong...
_________________
Bus Motor Build

What’s That Noise?!?

[richparker]

[cdennisg]

[Xevin]

[Spike0180]

[Abscate]

[airschooled]