S2T2

Jim Randell 8:25 am on 5 December 2025 Permalink Reply
Tags: by: Andrew Skidmore ( 85 )   

• 

  Jim Randell 8:26 am on 5 December 2025 Permalink | Reply

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

  It runs in 78ms. (The internal runtime of the generated code is 1.2ms).

  #! python3 -m enigma -rr
  
  SubstitutedExpression
  
  "XMAS + TREE = FAIRY"
  
  "is_triangular(TREE)"
  
  --answer="XMAS"
  

  Solution: XMAS = 7209.

  The sum is: 7209 + 3655 = 10864.

  And: TREE = 3655 = tri(85) = sum(1..85).

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• 

  Ruud 2:14 pm on 5 December 2025 Permalink | Reply

  To run this code, istr 1.1.12 is required.

  import peek
  import istr
  
  for tree in istr.range(1000, 10000):
      if tree.is_triangular():
          t, r, e, e0 = tree
          if e == e0 and tree[:3].all_distinct():
              digits_without_tree = set(istr.digits()) - {t, r, e}
              for x, m, a, s, f, i, y in istr.permutations(digits_without_tree):
                  if (xmas := x | m | a | s) + tree == (fairy := f | a | i | r | y):
                      peek(xmas, tree, fairy)
  

  More compact, but much less efficient:

  import peek
  import istr
  
  for x, m, a, s, t, r, e, f, i, y in istr.permutations(istr.digits()):
      if (tree := t | r | e | e).is_triangular() and (xmas := x | m | a | s) + tree == (fairy := f | a | i | r | y):
          peek(xmas, tree, fairy)
  

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• 

  CB Root 6:19 pm on 14 December 2025 Permalink | Reply

  Here is some (rather amateurish) Javascript code for your delectation:

  function myFunction() {
    
    var carry;
    var s,e,y;
    var SE;
    var a,r;
    var AE;
    var m,i;
    var x,t;
    var XT;
    var f;
    var XMAS,TREE,FAIRY;
  
    for(s=0;s<=9;s++){
      for(e=0;e<=9;e++){
        SE = s+e;
        y=SE%10;
        if(y>=0 && y<=9){
          carry=Math.floor(SE/10);
          for(a=0;a<=9;a++){
            AE=carry+a+e;
            r=AE%10;
            if(r>=0 && r<=9){
              carry=Math.floor(AE/10);
              for(m=0;m<=9;m++){
                i = carry + m + r;
                carry=Math.floor(i/10);
                if(i>=0 && i<=9){
                  for(x=1;x<=9;x++){
                    for(t=0;t<=9;t++){
                      XT = carry + x + t;
                      if(XT%10==a){
                        for(f=1;f<=9;f++){
                          if(allUnique([s,e,y,a,r,m,i,x,t,f])){
                            XMAS = parseInt(x.toString()+m.toString()+a.toString()+s.toString());
                            TREE = parseInt(t.toString()+r.toString()+e.toString()+e.toString());
                            FAIRY = parseInt(f.toString()+a.toString()+i.toString()+r.toString()+y.toString());
                            if(isTriangular(TREE)){
                              if(FAIRY==(XMAS+TREE)){
                                Logger.log(' xmas= '+x.toString()+m.toString()+a.toString()+s.toString());
                                Logger.log(' tree= '+t.toString()+r.toString()+e.toString()+e.toString());
                                Logger.log('fairy= '+f.toString()+a.toString()+i.toString()+r.toString()+y.toString());
                              }
                            }
                           }
                        }
                      }
                    }
                  }
                }
              }
            }
          }
        }
      }
    }
  }
  
  function allUnique(arrVal){
  
    var al = arrVal.length-1;
  
    var pp,qq;
  
    for(pp=0;pp<=al;pp++){
      for(qq=0;qq<=al;qq++){
        if(pp!=qq){
          if(arrVal[pp]==arrVal[qq]){
            return false;
          }
        }
      }
    }
    return true;
  }
  
  function isTriangular(testNo){
  
    var product = testNo * 8;
    product = product + 1;
    if(Math.sqrt(product)==Math.floor(Math.sqrt(product))){
      return true;
    }
    else{
      return false;
    }
  }
  

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  • 

    Jim Randell 8:59 am on 15 December 2025 Permalink | Reply

    Hi, thanks for leaving a comment.

    Unfortunately I’m not sure your code made it through the WordPress comments system unscathed. (Unprotected code often loses sections between < and > before I see it and cannot be fixed).

    If you leave a comment with your code between:

    [code]
    <your code here>
    [/code]

    I will fix it up in the original comment.

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• 

  CB Root 11:46 am on 15 December 2025 Permalink | Reply

  OK, sorry about that. Here follows my (slightly updated ) code bracketed as requested.

  [see code above]

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• 

  GeoffR 3:08 pm on 15 December 2025 Permalink | Reply

  
  % A Solution in MiniZinc
  include "globals.mzn";
  
  % Check TREE is a 4-digit triangular number
  var 1..140: n;
  
  constraint TREE = n * (n + 1) div 2;
  constraint TREE >= 1000 /\ TREE <= 9999;
  
  var 1..9:X; var 1..9:T; var 1..9:F; var 0..9:M;
  var 0..9:A; var 0..9:S; var 0..9:R; var 0..9:E;
  var 0..9:I; var 0..9:Y;
  
  constraint all_different ([X,T,F,M,A,S,R,E,I,Y]);
  
  var 1000..9999:XMAS = 1000*X + 100*M + 10*A + S;
  var 1000..9999:TREE = 1000*T + 100*R + 11*E ;
  var 10000..99999:FAIRY = 10000*F + 1000*A + 100*I + 10*R + Y;
  
  constraint XMAS + TREE == FAIRY;
  
  solve satisfy;
  output ["XMAS = " ++ show(XMAS) ];
  
  % XMAS = 7209
  % ----------
  % ==========
  
  
  

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