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Guest Message by DevFuse

# Closed form expression on steroids

Best Answer Prime, 29 January 2013 - 06:46 AM

But they don't need to be integers, those 11 periodic values.

Spoiler for one messy solution

Go to the full post

10 replies to this topic

### #11 Prime

Prime

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Posted 29 January 2013 - 10:42 PM

Funny.   I felt uncomfortable about using such complex math as Lagrange Interpolating Polynomial while not remembering how it actually worked.

I set out to invent a simpler switching function, which would select one value out of 11 based on an integer variable N and then convert that value into an integer of my choice. And I have invented such formula!   Thereafter, I consulted a respectable mathematical reference website and discovered that my simple and beautiful switching function was the Lagrange Interpolating Polynomial! Now I understand how it works! It appears 18th century mathematicians (Waring and Euler) invented it just for this puzzle.

I shall give a better explanation the puzzle solution and Lagrange Polynomial. It could be useful to some math students and, perhaps, parents of high school students who are about to get bogged down in those dreaded AP math classes.

Spoiler for Lagrange Interpolating Polynomial

Lagrange Polynomial: http://mathworld.wol...Polynomial.html

Edited by Prime, 29 January 2013 - 10:43 PM.

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Past prime, actually.

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