Project Euler Forum

msg6700 wrote: Wed Jan 25, 2017 10:00 am can anyone explain why "5 1 3 4 3 2 6 2 1" isn't true in "magic" 3-gon ring ??

Because you start with the lowest of the outside numbers. In this case that's 4, so that arrangement can only be described by "4 3 2 6 2 1 5 1 3".

This was pencil and paper. The sum of the digits in the five trios is 55 + the sum of the centre 5 digits which are also a multiple of 5 and can be 15+55, 20+55, 25+55... 40+55 corresponding to trio totals 14-19.
If lead digit is 6, inner pentagon is 12345 in some order , and obviously each line sums to 14 in this case.
To implement as a program once the logic is defined seems just silly, and a sledgehammer approach seems even sillier. On the other hand we could perhaps program for the six trio sum values 14-19, and that might be a challenge.

I have found four 16-digit solutions, and indeed the maximum among these have been accepted as the correct answer.

However, the problem states that it is also possible to have a 17-digit solution. I'm trying to find this 17-digit solution and I can't seem to find it. A 17-digit solution would mean that 10 is in an inner node. Is there really a 17-digit solution?

plapidez wrote: Wed Mar 05, 2025 8:24 am Is there really a 17-digit solution?

Yes, there are 8 of them.

(Sent example via PM.)

TripleM wrote: Tue Mar 25, 2025 1:02 am

plapidez wrote: Wed Mar 05, 2025 8:24 am Is there really a 17-digit solution?

Yes, there are 8 of them.

Can you give one of them?