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 re(2): My best @ jer and CH by Charlie)

Rather than check every possibility, some boards make more sense to check than others and some are repeats.

You might try the 9! boards with

nnnn
XXXn
XXnn
nXXn

for example, but this is the same as moving the number in the lower left either one space up or right.  Also on this board switching the two bottom numbers doesn't change the ratio.

 

Posted by Jer on 2016-03-15 09:38:52