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.

Consider this:

2143
9XX8
7XX6
XX5X

r=(2143+9+8+7+6+5)/(297+1+4+5+386)

r=2178/693=22/7

This approximation's  error is slightly below 0.04025 %

Still I'm sure one can do better.

Good luck!

Edited on March 15, 2016, 2:44 am

Posted by Ady TZIDON on 2016-03-14 14:32:35