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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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Digit Perms | Comment 10 of 13 |
Staying with Jer’s layout of the Xs, a computer
search through all permutations of the digits
gives the following optimum.

7512
xxx3
xx48
6xx9

7578/2412 = 3.141791045

which is 0.00019839.. too big.      (now corrected)

So perhaps we now need some rationale on the distribution of Xs.


Edited on March 16, 2016, 11:36 am
  Posted by Harry on 2016-03-15 11:23:43

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