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've spent exactly 45 min, trying to get close to PI, using only one of C(16,7) possible crossword forms and using common sense and calculator only.
I stop at 3.13888888... i.e, 0.086% error.
My (so far the only) solution should be a yardstick, so only the distributions of numbers and X's that produce a ratio r closer to PI should be submitted.
I am confident that this "record" will have a very short life.
Btw, I did not use Charlie's ratios, which might be helpful.