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# Penny's triple play

## Question

I put a handful of pennies on the table and I wondered whether I could group them so that each penny touched three and only three of the others. It took a while but I found it was possible. I then wondered whether I could do it with fewer pennies. It was clear that I could not.

How many pennies were in the group?

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I can put 16, but I'll bet there's a better solution.

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Is it required for each coin to touch fully table surface with one of its faces?

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Could do it with 4 pennies. Three flat on the table in a triangle and the fourth one on top of them in the middle.

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good solve, prime!

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Can you prove, that required arrangement is not possible with odd number of coins?

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Construct a graph where each node [penny] has three edges.

Perforce each edge connects two nodes. Thus

3n = 2e.

n must be even.

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Could do it with 4 pennies. Three flat on the table in a triangle and the fourth one on top of them in the middle.

Outside the box; off the table.

Honorable Mention for sure.

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Construct a graph where each node [penny] has three edges.

Perforce each edge connects two nodes. Thus

3n = 2e.

n must be even.

Completely off the topic, a technical issue. I cannot see the contents of the spoiler in the post. It appears as empty line. When I "quote" the post, the spoiler becomes visible inside the "quote".

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There do seem some irregularities with the site. I can see the contents.

You might send a PM to Rookie1ja with your specifics.

I would have, instead of this post, but I don't know how simultaneously to PM to two people.

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There do seem some irregularities with the site. I can see the contents.

You might send a PM to Rookie1ja with your specifics.

I would have, instead of this post, but I don't know how simultaneously to PM to two people.

Lol...there's the convenient 'Other Recipients' field...send as 'Invitation' to include multiple ppl...

...or are you trolling? ;P

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There do seem some irregularities with the site. I can see the contents.

You might send a PM to Rookie1ja with your specifics.

I would have, instead of this post, but I don't know how simultaneously to PM to two people.

Lol...there's the convenient 'Other Recipients' field...send as 'Invitation' to include multiple ppl...

...or are you trolling? ;P

Thanks. It's amazing what one can learn simply by admitting ignorance.

Scratch one excuse!

Trolling? I recall, from my Norwegian heritage, learning about these delightful creatures that would not allow passage without cost. These were the first troll bridges I guess.

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