# Electrical brain-teaser/puzzle. Just for fun

Paul Owner/Technician California Posted   Latest   Edited

This one seems to have fizzled out, so I've attached the solution to my question inductor puzzle. It seems really simple once you look at the diagram.

I've also the diagram of the … Prius smart key I've been working on in case anybody ever needs it.

Finally, I attached the solution to the resistor cube puzzle that Kerry brought up, which was a much more difficult puzzle, for me at least. Even knowing that the answer was 5/6 of the resistor value, it took me hours to figure out how. Basically, the current must exit each of the two corners through three resistors in parallel. Between the two corner segments are 6 resistors in parallel (which was the hardest for me to conceptualize).

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I've been working on reverse engineering a smart-key circuit board while stuck in the office answering phones to stave off boredom and learn more about electronics.

There's an inductor with two windings at 90 degrees and 4 terminals (see picture). I've made a circuit diagram of the board and when I got to this section, I wondered how I'd figure out how this inductor is wound, and that's today's puzzle. I believe that I have figured it out, but I had fun doing so, so maybe you will too.

I've attached a diagram with my measurements in ohms and milli-henrys. This will probably be too easy for some, but if you're like me it will take a little work to figure out. Post your winding diagram once you're done. (Like an alternator would appear in a wiring diagram). I've labeled the terminals 1, 2, 3, and 4 to make it easier to diagram.

Paul

Edit: I handed this to a few guys at the shop and the most frequent question was, “What do you mean by diagram?”. I've attached an example diagram of a motor winding as an example. It's a delta winding with a high leg. Hope that helps explain.

Edit 2: Here are some hints.

The longer the wire is the higher it's resistance. Trying to use the inductance measurements confuses things because one winding can induce a field in another winding and change its own measurement, so I used the DC resistance measurements only.

I drew the resistance measurements as lines and then tried to arrange them so they would have 4 terminations that lined up. Lines can be bent like a string. A termination can be added at any point along the lines.

There are 6 measured resistances: 54, 54, 108, 140, 194, and 194.

54 + 54 =108

54 + 140 = 194

See the new picture in green pen. Good luck :)

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Interesting
Dan Owner/Technician
Texas
Dan

… I must be living under a rock… I thought you were kidding with the millihenry thing … Mr. Google says it is REAL … I'll go crawl back under my rock and pout… Dan H. … Hobbs … South Texas …

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Funny
Off Topic
Geoff Diagnostician
Hawaii
Geoff

The only thing I remember about this stuff is "right hand rule" ... but there is also a "left hand rule" !!! Electrical physics was 25 years ago and I haven't used it since.

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Jeffrey Mobile Technician
Illinois
Jeffrey

This is challenging. I might need a day or two to figure it out.

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Dmitriy Analyst
Ontario
Dmitriy

Two windings? I thought there should be three (for it to be a 3D antenna).

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Agree
Paul Owner/Technician
California
Paul

I don't know. I can see two windings and I've come up with a way that they can be connected that makes sense to me. There are 4 terminals, so two windings could be used like 3.

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Matthew Diagnostician
Kentucky
Matthew

Curious if the lower resistance coil is used to excite the higher resistance coil to amplify or tune the output signal. with them being over top of one another this being what 900 mhz signal this will take some time lol

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Paul Owner/Technician
California
Paul

I don’t have the answer to your question about how it works. I wish I did. One day I hope to :) This is from a Gen2 Prius. Oscillators on the car transmit the vehicle ID to the key at 134 KHz. If the key recognizes the vehicle ID, it responds at 315MHz. There are 4 antennas on the board. 3 are small SMD antennas. This is the largest antenna. I don’t know it’s role though. It seems one of the…

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Robert Technician
Michigan
Robert

Definitely gotta be right hand rule know matter how you grip it, has to be & possibly Lentz law but i didn't see a magneto or an IC

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Kerry Mobile Technician
Ohio
Kerry

Lol…The right hand and left hand rules are to determine the direction of thrust or motion when introducing a current carrying conductor to a magnetic field. The right hand rule is for generators where you are producing electricity and (Fleming's) left hand rule is for motors where you are producing motion.

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Jon Owner/Technician
California
Jon

The real question is how many phone calls went unanswered while you geeked out on that circuit board:}?

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Funny
Paul Owner/Technician
California
Paul

That's funny :) I do something unimportant while answering calls so I can stop without losing my place and messing something important up. That said it's still annoying when the phone rings and I lose my place :)

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Kerry Mobile Technician
Ohio
Kerry

Paul, some of us might need more context to help noodle on this. You mentioned that it's a smart key circuit board. Can you give more background like whether this is involved with the anti-theft system or the remote keyless entry system?

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Paul Owner/Technician
California
Paul

I don't actually know the function of the antenna. It might be for transmitting or receiving. It might be for a 125KHz or the 315KHz signal. The smart key is tied to the keyless entry, security, and immobilizer systems. On this car the Smart Key ECU is the component that interacts directly with the key … Prius). I'll edit my original post to add a hint on how I figured it out. It's…

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Matthew Diagnostician
Kentucky
Matthew

Just for reference, if its a proximity key the antenna should operate on a much higher frequency. Generally well above the normal 315mhz were used to seeing. id say the key transmits and receives on two different frequency. One for the keyless entry and one for the antitheft.

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Kerry Mobile Technician
Ohio
Kerry

I understand, it was just a curiosity question. This problem reminds me of the resistor cube problem, if you're familiar that…(All 12 sides of a cube have a 1 ohm resistor, and the challenge is to figure out the net resistance from one corner to the long diagonal opposite corner)

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Paul Owner/Technician
California
Paul

Without building it I assume. That sounds fun I’ll give it a try :) wait. 12 sides? 6 sides and 8 corners right?

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Jeffrey Mobile Technician
Illinois
Jeffrey

Well I have a migraine and doing it quick in my head, I get 3 ohms

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Jeffrey Mobile Technician
Illinois
Jeffrey

Let me correct that. 1 ohm. I think

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Paul Owner/Technician
California
Paul

So that was fun, but disappointing. There are 6 paths corner to corner. Each path flows through 3, 1-ohm resistors for a total of 3 ohms per path. The 6 paths are in parallel, so ⅓ + ⅓ + ⅓ +⅓ + ⅓ + ⅓ = 6/3. So, the resistance from corner-to-corner ought to be 2 ohms…. at least that's what I thought until I checked to see if I was right. I wasn't

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Kerry Mobile Technician
Ohio
Kerry

Yes I used to give it to my students to see who was thinking and who was just learning the math. It kind of forces the concept of equipotential nodes to be recognized and resolved…and of course the “path of least resistance” concept helps weed out implausible answers. I'm glad it was interesting if nothing else!

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Stephen Technician
Tennessee
Stephen

youtu​.​be/Eoh-JKVQZwg Solution to equal resistor cube.

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Dmitriy Analyst
Ontario
Dmitriy

This is a different one — between A and H? The classic one would be between A and G?

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