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Subject: Engine Problem - My Brain Hurts rss

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Ian Wakeham
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Help me regain my sanity.

The following (blurry) image is from my 8 year old boy's puzzle book.

From gallery of batdog


However, nobody in the house can get the "correct answer", according to the book.

The book answer is:
Spoiler (click to reveal)
OFF

We think:
Spoiler (click to reveal)
ON

Who is right?
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Ian Wakeham
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BTW, the direction for each cog I get (in order) is as follows, based on L (anticlockwise) and R (clockwise):
Spoiler (click to reveal)
L R L R R L R L R L R L R L L R R L
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Josh Jennings
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I'm thinking that the book is wrong and you are correct. The simpler way to look at it is this:

Spoiler (click to reveal)

Each connected gear will change direction.
Each crossed band will also change direction.
Each non-crossed band will maintain direction.
Counter-clockwise = on, clockwise = off.

Moving the handle, you get this sequence:
Counter->Clock->Counter->Clock->Clock->Counter->Clock->Counter->Clock->Counter->Clock->Counter->Clock->Counter->Counter->Clock->Clock->Counter.

The result should be Coutner-clockwise = On.
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Yeah the book is wrong.
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The solution to this situation is obvious. You must build the cog/pulley engine in real life.
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I get "ON" as well.
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You know what happened... the illustrator drew the drawings and handed them over to the company. They assigned them to Bob who was tasked with figuring out which answer was right. Bob did a bunch of them and at the end of a long day, Bob got this one wrong. The company had Jim double check Bob's work to verify that he got the right answer.

Jim did a good job doublechecking Bob's work, but quickly realized he was putting in a lot of work and every single time it turned out that Bob was right. He realized that it was a lot easier to skip all the hard work and just agree that Bob was right. After all, the worst thing that would happen is that it would get printed and six months down the line someone would complain about it. Would they really come back and chastise him about it? Would he even still be there by then?
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I have done it about 5 times, and I keep getting OFF.

Are you counting the first cog as a cog or just the lever to activate it?
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demondude777 wrote:
I have done it about 5 times, and I keep getting OFF.

Are you counting the first cog as a cog or just the lever to activate it?
The drawing made me think that the lever is welded to the cog, so moving the level and moving the cog are one and the same.
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wmshub wrote:
demondude777 wrote:
I have done it about 5 times, and I keep getting OFF.

Are you counting the first cog as a cog or just the lever to activate it?
The drawing made me think that the lever is welded to the cog, so moving the level and moving the cog are one and the same.
Correct...me too. There are 18 total. Thus if the first one starts counter, like it looks like the image is implying, then the last one would rotate clockwise...towards off.

It order for the first one to go the same direction as the last...there would have to be an odd #.
 
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demondude777 wrote:


It order for the first one to go the same direction as the last...there would have to be an odd #.
You're very much missing that the cogs are not all directly connected, some are belt and some are cross belt.
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Geosphere wrote:
demondude777 wrote:


It order for the first one to go the same direction as the last...there would have to be an odd #.
You're very much missing that the cogs are not all directly connected, some are belt and some are cross belt.
I wasn't. I was taking that into consideration too, and still getting an off outcome.

I just went back and checked a couple times and now I am getting on over and over. I think I miscounted the ones that weren't crossed initially.

At this point:

External image


Edit: Maybe by "pushing to the left" means spinning to the left to cause the first gear to go clockwise. That definitely gets me an off outcome. Poor wording?
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There are 18 cogs, with 17 interconnections.

teeth-teeth interconnections change the direction. Twisted band connections change the direction. Untwisted connections keep the same direction

So, let us define "clockwise" as 1, and anticlockwise as "-1". Let us define a change of direction operation as "multiply by -1" (If, in a pair of cogs, the first is anticlockwise, then multiplying by -1 makes the next cog 1 = clockwise, and vice versa) and a "no change of direction" as "multiply by 1"

There are 3 untwisted interconnections, leaving 14 connections that change the direction.

So the first cog is -1, and the last cog is -1 * (all the operations)

The order of those operations is unimportant, so it's -1 * (1^3 * (-1^14))

1^3 = 1

-1^2n (where n is a positive integer) = 1

so it's -1 * 1 * 1 = -1

The final cog is -1, or anticlockwise, so will point to ON.
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These kinda of problems are so simple: just move your finger in the direction of rotation of each gear. If it touches another gear, that gear will be going the other direction. If it touches a rubber-band, just trace the rubber band line to the next gear.

Doing this, I get that the indicator will move towards OFF. So yeah, the book's answer is correct.

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kswingruber wrote:

These kinda of problems are so simple: just move your finger in the direction of rotation of each gear. If it touches another gear, that gear will be going the other direction. If it touches a rubber-band, just trace the rubber band line to the next gear.

Doing this, I get that the indicator will move towards OFF. So yeah, the book's answer is correct.

Okay. I followed this method, but got ON for my answer. In fact, I traced it so that you can check my work:

Spoiler (click to reveal)
From gallery of thermogimp
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I also get ON.
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thermogimp wrote:
kswingruber wrote:

These kinda of problems are so simple: just move your finger in the direction of rotation of each gear. If it touches another gear, that gear will be going the other direction. If it touches a rubber-band, just trace the rubber band line to the next gear.

Doing this, I get that the indicator will move towards OFF. So yeah, the book's answer is correct.

Okay. I followed this method, but got ON for my answer.
I think it depends on which way the first one spins. Are you spinning it clockwise or counter clockwise?

NM just saw your pic....try spinning it clockwise. I think the turn to left means it spins that way too.
 
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demondude777 wrote:

I think it depends on which way the first one spins. Are you spinning it clockwise or counter clockwise?

NM just saw your pic....try spinning it clockwise. I think the turn to left means it spins that way too.
For sure, changing the direction of the first gear will change the answer. I just happen to think that the arrow to the left means spin the gear counter-clockwise since it's above the gear, but I can see where there may be confusion. They probably should have drawn a circular arrow to remove all doubt.
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thermogimp wrote:
demondude777 wrote:

I think it depends on which way the first one spins. Are you spinning it clockwise or counter clockwise?

NM just saw your pic....try spinning it clockwise. I think the turn to left means it spins that way too.
For sure, changing the direction of the first gear will change the answer. I just happen to think that the arrow to the left means spin the gear counter-clockwise since it's above the gear, but I can see where there may be confusion. They probably should have drawn a circular arrow to remove all doubt.
I think it's pretty clear as it is.
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I got ON also. I cannot see how pushing the first handle to the left could possibly spin the gear clockwise. The handle is attached to the center of the gear at a right angle, parallel with the surface of the gear; if you push the handle left, the top of the gear goes left, so the whole gear turns counter-clockwise.

The picture with the green trace path shows very clearly what happens. Thanks for that picture.

Would anyone like to explain how they see the first gear turning clockwise, because I cannot see it. Is it a perception thing, like the vase-or-two-faces optical illusion? robot
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thermogimp wrote:
kswingruber wrote:

These kinda of problems are so simple: just move your finger in the direction of rotation of each gear. If it touches another gear, that gear will be going the other direction. If it touches a rubber-band, just trace the rubber band line to the next gear.

Doing this, I get that the indicator will move towards OFF. So yeah, the book's answer is correct.

Okay. I followed this method, but got ON for my answer. In fact, I traced it so that you can check my work:

Spoiler (click to reveal)
From gallery of thermogimp
I agree with your green line. Well done.
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I get ON as well.
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On.
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demondude777 wrote:
NM just saw your pic....try spinning it clockwise. I think the turn to left means it spins that way too.
The big arrow by the first gear suggests anti/counter-clockwise, so ON.

I did the same tracing thing with my mouse pointer. ON.

As said, there are 18 gears. A mesh or a figure-8 band reverses direction. An O-band maintains direction. With 18 gears, there are 17 connections. Minus the 3 O-bands that do nothing, leaves 14 reverses. Each pair of reverses maintains direction (parity), so 7 pairs (14) maintain the direction of the initial gear, counter-clockwise, toward ON.
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