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".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 ??
Problem 068
Forum rules
As your posts will be visible to the general public you are requested to be thoughtful in not posting anything that might explicitly give away how to solve a particular problem.
This forum is NOT meant to discuss solution methods for a problem.
See also the topics:
Don't post any spoilers
Comments, questions and clarifications about PE problems.
As your posts will be visible to the general public you are requested to be thoughtful in not posting anything that might explicitly give away how to solve a particular problem.
This forum is NOT meant to discuss solution methods for a problem.
In particular don't post any code fragments or results.
Don't start begging others to give partial answers to problems
Don't ask for hints how to solve a problem
Don't start a new topic for a problem if there already exists one
Don't start begging others to give partial answers to problems
Don't ask for hints how to solve a problem
Don't start a new topic for a problem if there already exists one
See also the topics:
Don't post any spoilers
Comments, questions and clarifications about PE problems.
-
DJohn
- Posts: 90
- Joined: Sat Oct 11, 2008 12:24 pm
Re: Problem 068
-
laogui
- Posts: 7
- Joined: Tue Jun 06, 2023 3:05 pm
Re: Problem 068
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.
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.
-
plapidez
- Posts: 2
- Joined: Fri Feb 14, 2025 5:43 am
Re: Problem 068
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?
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?
-
TripleM
- Posts: 384
- Joined: Fri Sep 12, 2008 3:31 am
Re: Problem 068
Yes, there are 8 of them.
(Sent example via PM.)
Last edited by TripleM on Tue Apr 01, 2025 1:57 am, edited 1 time in total.
-
plapidez
- Posts: 2
- Joined: Fri Feb 14, 2025 5:43 am