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: Sr=489+(56+7)+1+32=585.
Same operation per column: Sc= 513+(46+2)+8+97=666
Evaluate the ratio r= Sr/ Sc=585/666= 0.878378...
Your task :
Distribute the 9 non-zero digits and 7 black squares in a 4x4 grid so
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.
I wondered if the previous distribution of Xs was
unnecessarily limiting the totals and reducing the options,
so I’ve moved them into one corner. It seems to have
produced a better result (searching over all perms of the digits) -but with smaller totals!.
6390/2034 = 3.14159292035….
Too big by 0.0000002667..
Posted by Harry
on 2016-03-15 12:16:41