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To-day is Monday & a PIday (Posted on 2016-03-14) Difficulty: 4 of 5
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
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.

No Solution Yet Submitted by Ady TZIDON    
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Hints/Tips a start : a solution that must be improved | Comment 2 of 13 |

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

2987
3XX1
6X54
XXXX

(2987+3+1+6+54)/(236+9+8+5+714)=3051/972=3.138888...

I am confident that this "record"  will have a very short life.

Btw, I did not use Charlie's ratios, which might be helpful.


 


  Posted by Ady TZIDON on 2016-03-14 14:01:24
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