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Jim Randell 11:28 am on 2 March 2023 Permalink Reply
Tags: by: J M Leonard   

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  Jim Randell 11:30 am on 2 March 2023 Permalink | Reply

  We can label the 8 areas of the corresponding Venn diagram according to who likes who:

  (Jane) = a
  (Jean) = b
  (June) = c
  (Jane + Jean) = d
  (Jean + June) = e
  (Jane + June) = f
  (Jane + Jean + June) = g
  () = x

  and we have:

  a + b + c + d + e + f + g + x = 100
  a + d + g + f = 58
  b + e + d + g = 45
  c + e + f + g = 42
  d + g = 27
  g + f = 28
  e + g = 19
  g = 18

  These equations are easily solved manually to give:

  g = 18
  e = 1
  f = 10
  d = 9
  a = 21
  b = 17
  c = 13
  x = 11

  Solution: 11 of the boys were not fans of any member of the group.

  ---

  Here is a program using the [[ Matrix() ]] class from the enigma.py library.

  Run: [ @replit ]

  from enigma import (Matrix, as_int, printf)
  
  # construct the equations
  eq = Matrix.equation("abcdefgx")
  eqs = [
    eq("abcdefgx", 100),
    eq("adgf", 58), eq("bedg", 45), eq("cefg", 42),
    eq("dg", 27), eq("gf", 28), eq("eg", 19),
    eq("g", 18),
  ]
  
  # solve the equations
  (a, b, c, d, e, f, g, x) = Matrix.linear(eqs, valid=(lambda n: as_int(n, "0+")))
  
  # output the solution
  printf("x={x} [a={a} b={b} c={c} d={d} e={e} f={f} g={g}]")
  

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