S2T2

Jim Randell 8:56 am on 20 May 2021 Permalink Reply
Tags: by: Alan Bergson ( 4 )   

• 

  Jim Randell 8:56 am on 20 May 2021 Permalink | Reply

  We can get a solution using the [[ SubstitutedExpression ]] solver from the enigma.py library.

  This run file executes in 421ms.

  #! python3 -m enigma -rr
  
  SubstitutedExpression
  
  "abs(SUNDAY - TEASER) = EASTER"
  
  "E < S" # EASTER < SUNDAY
  "E < T" # EASTER < TEASER
  
  --answer="SUNDAY"
  

  Solution: SUNDAY = 816270.

  ---

  For a faster solution we can use the (experimental) [[ SubstitutedExpression.split_sum() ]] solver.

  The following Python program runs in 58ms.

  Run: [ @replit ]

  from enigma import SubstitutedExpression, printf
  
  # solve the sum <expr>
  def check(expr, *extra):
    p = SubstitutedExpression.split_sum(expr, extra=extra, answer="SUNDAY").solver()
    for (s, ans) in p.solve(verbose=0):
      printf("SUNDAY = {ans} [{expr} / {s}]", s=p.substitute(s, expr))
  
  # check the two possibilities
  check('EASTER + SUNDAY = TEASER', 'E < S')
  check('EASTER + TEASER = SUNDAY', 'E < T')
  

  ---

  There is only one possible solution even without the information that EASTER is the lowest number. So the [[ E < S ]] and [[ E < T ]] clauses could be removed.

  LikeLike

• 

  GeoffR 9:58 am on 31 May 2021 Permalink | Reply

  % A Solution in MiniZinc
  include "globals.mzn";
  
  var 1..9: E; var 0..9: A; var 1..9: S;
  var 1..9: T; var 0..9: R; var 0..9: U;
  var 0..9: N; var 0..9: D; var 0..9: Y;
  
  constraint all_different ([E,A,S,T,R,U,N,D,Y]);
  
  var 100000..999999: EASTER = 100000*E + 10000*A + 1000*S + 100*T + 10*E + R;
  var 100000..999999: SUNDAY = 100000*S + 10000*U + 1000*N + 100*D + 10*A + Y;
  var 100000..999999: TEASER = 100000*T + 10000*E + 1000*A + 100*S + 10*E + R;
  
  constraint EASTER < SUNDAY /\ EASTER < TEASER;
  constraint EASTER + TEASER == SUNDAY \/ EASTER + SUNDAY == TEASER;
  
  solve satisfy;
  output ["SUNDAY's number = " ++ show(SUNDAY) ];
  % SUNDAY's number = 816270
  % ----------
  % ==========
  
  
  

  LikeLike