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 No Subject by Harry)

Nice. 

Now that I think about it my suggested x-distribution was from trying to hit one of Charlie's goals by hand.  This is easier if there is just one large number and many small ones.  It turned out to still be too hard to hit numerator and denominator simultaneously but I got lucky and found a close one.

(Incidentally you misplaced the decimal in comparing your first solution: 7478/2412 is only off by .000198)

Posted by Jer on 2016-03-15 13:45:13