S2T2

Jim Randell 9:07 am on 24 July 2026 Permalink Reply
Tags: by: Victor Bryant ( 150 )   

• 

  Jim Randell 9:08 am on 24 July 2026 Permalink | Reply

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

  It runs in 108ms. (Internal runtime is 34ms).

  from enigma import (SubstitutedExpression, irange, union, diff, seq2str, printf)
  
  #  A B C
  #  D E F
  #  G H I
  
  # possible numbers in the grid
  N = 199
  digits = irange(1, N)
  
  # we have E = 100
  # 1 is either placed in a corner (A) or edge (B)
  
  # magic constant is 3E = 300
  eqs = [
    "A + B + C == 300", # row 1
    "D + E + F == 300", # row 2
    "G + H + I == 300", # row 3
    "A + D + G == 300", # col 1
    "B + E + H == 300", # col 2
    "C + F + I == 300", # col 3
    "A + E + I == 300", # diag 1
    "C + E + G == 300", # diag 2
  ]
  
  # consider placing 1 at A or B
  for q in "AB":
  
    # make a puzzle for this magic square
    p = SubstitutedExpression(
      eqs,
      base=N + 1, digits=digits,
      s2d={ 'E': 100, q: 1 },
      verbose='',
    )
  
    # collect all numbers that can appear in the square
    ns = union(s.values() for s in p.solve())
  
    # most numbers should be possible
    if not (2 * len(ns) > N - 2): continue
  
    # output impossible numbers
    xs = diff(digits, ns)
    printf("{q}=1 -> impossible = {xs}", xs=seq2str(xs))
    printf()
  

  The 1 must be placed in an edge cell (i.e. not a corner cell), and then the following numbers cannot appear in a square:

  34, 67, 133, 166

  (Note that these form two pairs (34, 166) and (67, 133), each with a sum of 200).

  The most likely of these to be the age of someone who has a grandson interested in magic squares (so, maybe aged around 10), is 67.

  Solution: The setter is 67.

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• 

  Frits 5:11 pm on 25 July 2026 Permalink | Reply

  #  A B C
  #  D E F
  #  G H I
   
  # assume A = 1 or B = 1
  # A = 1 is invalid as it causes both C < 100 and G < 100 and C+E+G < 300
  # B = 1 leads to 
  
  #   A       1    299 - A
  # 399-2A   100   2A - 199
  # A - 99   199   200 - A 
  
  used = set()
  for a in range(101, 199):
    ns = {a, 1, 299 - a, 399 - 2 * a, 100, 2 * a - 199, a - 99, 199, 200 - a}
    # nine different positive whole numbers 
    if len(ns) == 9:
      used |= ns
  
  print(f"answer: {''.join(str(n) for n in range(45, 100) if n not in used)}")    
  

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