hitchyhawk / magicsquare Goto Github PK

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Around September 2019          
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This program is meant to find solutions to the squared magic square question:
More info:            http://www.multimagie.com/
Where I was inspired: https://youtu.be/aOT_bG-vWyg

- - - - - - - - - -
| a^2 | b^2 | c^2 |
|- - -|- - -|- - -|
| d^2 | e^2 | f^2 |
|- - -|- - -|- - -|
| g^2 | h^2 | i^2 |
- - - - - - - - - -

Where each Row, coloumn, and the two diagonals add up to the same number.

If you want to solve this your, program needs to be heavily optimized. 
If you think of this like a clock where "a" is seconds, "b" is minutes, and so on. It would take

60 seconds    for 1 minute
60 minutes    for 1 hour
24 hours      for 1 day
7  days       for 1 week
4  weeks      for 1 month (because I need more variables, and this is about time scale anyways)
12 months     for 1 year
10 years      for 1 decade
10 decades    for 1 centuary
10 centuries  for 1 millenium

Multiply that all together
= 10*10*10*12*4*7*24*60*60
= 29'030'400'000 seconds
Or another way to think of it is steps, and that was with relatively low upper limits before the next number goes up.
Now your computer may be pretty fast but even if it did 1000 steps a second.

you would still have to wait a long time
29'030'400 seconds

This is where an adjustment to strategy comes into play. 
Nearly all those combinations that we checked dont even add up to the same number, or ever will. 

This program instead finds combinations of numbers such that:
a^2 + b^2 + c^2 = x
for any x I specify

Then it places these combinations into a list in the form:
{a,b,c}

From the original board theres a few things we need to note 
a is used three times
b is used two   times
c is used three times
e is used four  times

Everything else is just rotations of this, but what we can take away is:
anything that is used ONLY once must not be apart of the final answer.
if a set has EACH of its three elements only USED ONLY TWICE means it must not be apart of the final answer.

Those are our two rules. 
From there we can start removing useless pairs from our set, which will show us more pairs that can be taken out.
We are trimming down the possibilities. 

This method let me check all pairs of x under 300k after that it started to slow down. But for checking x under 100k is incredibly fast.

I made this code a long time ago so it has some memory leaking errors 
This will not be fixed because there is no need for this code. From what I linked above people have said:
From Lee Morgenstern "if there is a 3x3 magic square of distinct squares, then all entries must be above 10^14."
link to the quote http://www.multimagie.com/English/SquaresOfSquaresSearch.htm 
10^14 !! 
I have only check up to 3*10^5 and my program starts to slow down significantly.