S2T2

Jim Randell 8:19 am on 18 July 2025 Permalink Reply
Tags: by: Victor Bryant ( 139 )   

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  Jim Randell 8:20 am on 18 July 2025 Permalink | Reply

  There are 8 boxes to be filled out with a digit (from 0 to 9), and each of the digits 0 to 9 already occurs once before the boxes are filled out.

  The first six boxes count the 10 given digits, plus those in the 8 boxes, so must sum to 18.

  The first 2 boxes must contain 1 or more, and the next 4 boxes must contain 2 or more.

  And the box with the mean must also be 2 or more.

  Here is a solution using the [[ SubstitutedExpression ]] solver from the enigma.py library.

  The following run file executes in 95ms. (Internal runtime of the generated code is 16.8ms).

  Run: [ @codepad ]

  #! python3 -m enigma -rr
  
  SubstitutedExpression
  
  # let the 8 empty boxes be: A B C D E F G H
  --distinct=""
  --digits="1-9"
  --invalid="1,CDEFH"
  --macro="@boxes = [A, B, C, D, E, F, G, H]"
  
  # first 2 boxes
  "@boxes.count(0) + 1 = A"
  "@boxes.count(1) + 1 = B"
  
  # next 4 boxes
  "@boxes.count(2) + @boxes.count(3) + 2 = C"
  "@boxes.count(4) + @boxes.count(5) + 2 = D"
  "@boxes.count(6) + @boxes.count(7) + 2 = E"
  "@boxes.count(8) + @boxes.count(9) + 2 = F"
  
  # final 2 boxes
  "G in [A, B, C, D, E, F, H]"
  "iavg(@boxes) = H"
  
  --template="@boxes"
  --solution=""
  
  # [optional] additional constraints to improve run time
  # the sum of the first 6 boxes must be 18
  "A + B + C + D + E + F = 18"
  # we can't write 0 in any of the boxes, so there is only 1 zero
  --assign="A,1"
  

  Solution: The digits are: 1, 2, 8, 2, 2, 3, 3, 3.

  The statements then become:

  Number of occurrences of 0 = [ 1 ]
  Number of occurrences of 1 = [ 2 ]
  Total occurrences of 2s and 3s = [ 8 ]
  Total occurrences of 4s and 5s = [ 2 ]
  Total occurrences of 6s and 7s = [ 2 ]
  Total occurrences of 8s and 9s = [ 3 ]
  A digit you have written in another box = [ 3 ]
  The average of all your written digits = [ 3 ]

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  • 

    Frits 2:04 pm on 18 July 2025 Permalink | Reply

    @Jim, you can also add B in line 8 (ao because of line 32).

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