# Thread: New Year puzzle

1. ## New Year puzzle

I returned to something I've been thinking about lightly, off and on, for over the past 20 years and I've made a discovery last week which I'm giving to you in the form of a puzzle.

As you may know I specialize in magic squares. So my puzzle, which I'm starting off making it deliberately vague to make it challenging, is can you find a connection between quartic numbers and magic squares (of various sizes)?

I will give you a week to propose a solution to this problem and I may drop hints. If you can't find an answer within a month's time, then I'll post in the answer.

Happy New Year and good luck to you.

2. ## A hint

Originally Posted by wonderboy1953
I returned to something I've been thinking about lightly, off and on, for over the past 20 years and I've made a discovery last week which I'm giving to you in the form of a puzzle.

As you may know I specialize in magic squares. So my puzzle, which I'm starting off making it deliberately vague to make it challenging, is can you find a connection between quartic numbers and magic squares (of various sizes)?

I will give you a week to propose a solution to this problem and I may drop hints. If you can't find an answer within a month's time, then I'll post in the answer.

Happy New Year and good luck to you.
Too vague? Here's a helpful hint: consider any quartic number and its successor (e.g. $\displaystyle 1^4$ and $\displaystyle 2^4$
or $\displaystyle 3^4$ and $\displaystyle 4^4$).

3. ## With this hint, you're getting closer

Think about a formula that applies to magic squares (the formula is well known to magic square enthusiasts so you might do an internet search).

4. ## My final hint

Look at the absolute value of the difference between a quartic number and its successor quartic number and relate the difference to magic squares.

5. I've decided to make this puzzle and its solution part of my next article on magic squares coming out in the MHF Journal, Issue 4. Until then you will have to wait.