# Project Euler #312

Sometimes I wish I could share solutions to PE problems. They’re so great! I totally enjoyed every bit of this week’s puzzle. At first you don’t know where to start, it seems so complicated and then you just immense yourself in the pleasure of thinking and bit by bit everything becomes crystal clear so that in the end you can say “Hey! It was easy” 😀

– A Sierpiński graph of order-1 (S1) is an equilateral triangle.
– Sn+1 is obtained from Sn by positioning three copies of Sn so that every pair of copies has one common corner. Let C(n) be the number of cycles that pass exactly once through all the vertices of Sn.
For example, C(3) = 8 because eight such cycles can be drawn on S3, as shown below: It can also be verified that :
C(1) = C(2) = 1
C(5) = 71328803586048
C(10 000) mod 108 = 37652224
C(10 000) mod 138 = 617720485

Find C(C(C(10 000))) mod 138.

## 9 Comments

• Dan says:

I felt the same way when I first read this problem but I was surprised to find a very simple and elegant pattern. This was the first problem where I was able to submit a solution in the top 100.

You seem to be getting all of the latest euler problems. I’m wondering what’s your background?

• admin says:

What is Your background then? 🙂

• dfens says:

udalo mi sie wyprowadzic wzor ogolny, ale liczby są mega, mecze sie z tym od paru dni, gratuluje 😉

• swish says:

Please help me with this problem. I derived nice formulas for C(n), but i dont quite get it how to calculate C(C(C(10000))) mod 13^8 from there.

• admin says:

Think PE. It’s pretty obvious that this problem would be unsolvable if C(n) wasn’t… what? 😉

• swish says:

what? =

• Alex K says:

What does distinct mean here?

• Alex K says:

Opps wrong problem