The 9 numbers and 7 Xs of the set (1,2,3,4,5,6,7,8,9,X,X,X,X,X,X,X ) were placed in a 4x4 grid to create a matrix as follows:
X 4 8 9
5 6 X 7
1 X X X
3 2 X X
Consider the Xs as black squares in a crossword and evaluate the sum of the sums taken per row: S_r=489+(56+7)+1+32=585.
Same operation per column: S_c= 513+(46+2)+8+97=666
Evaluate the ratio r= S_r/ S_c=585/666= 0.878378...

Your task :
Distribute the 9 non-zero digits and 7 black squares in a 4x4 grid so
that the ratio r, calculated as in the example above will be as close
to the value of pi (=3.14159265…) as possible.

HaPPy Pi day, every Person.

(In reply to My best by Jer)

1. Cheers!  We have a new "record".   
Let's try to beat it!

2.  Absolute difference vs % :  None makes "more sense". One is 3.14 times the other, so in slang terms- "same difference."

3. @ Charlie. There are 16!/7! possible "crosswords". What is your estimate of runtime needed to exercise an exhaustive search using your hardware?

Posted by Ady TZIDON on 2016-03-15 01:55:56