Enigmatic Code

Programming Enigma Puzzles

Enigma 392: Nothing written right

From New Scientist #1542, 8th January 1987 [link]

In the following addition sum all the digits are wrong. But the same wrong digit stands for the same correct digit wherever it appears, and the same correct digit is always represented by the same wrong digit.

Find the correct addition sum.

[enigma392]

Advertisements

2 responses to “Enigma 392: Nothing written right

  1. Jim Randell 21 April 2017 at 7:18 am

    The SubstitutedSum() solver from the enigma.py library makes short work of this problem.

    This Python code runs in 41ms.

    from enigma import SubstitutedSum
    
    SubstitutedSum(
      ['7086', '2346'], '34654',
      d2i={ 0: '0237', 2: '2', 3: '3', 4: '4', 5: '5', 6: '6', 7: '7', 8: '8' }
    ).go()
    

    Solution: The correct sum is: 2465 + 8105 = 10570.

  2. geoffrounce 21 April 2017 at 8:51 am
    % A Solution in MiniZinc
    % Substituting letters for the wrong digits, the sum is:
    %  ABCD
    %+ EFGD
    % -----
    % FGDHG 
    % -----
    
    include "globals.mzn";
    
    var 1..9:A;  var 0..9:B;  var 0..9:C;  var 0..9:D; 
    var 1..9:E;  var 1..9:F;  var 0..9:G;  var 0..9:H; 
    
    constraint alldifferent([A,B,C,D,E,F,G,H]);
    
    var 1000..9999: ABCD = 1000*A + 100*B + 10*C + D;
    var 1000..9999: EFGD = 1000*E + 100*F + 10*G + D;
    var 10000..99999: FGDHG = 10000*F + 1000*G + 100*D + 10*H + G;
    
    constraint ABCD + EFGD == FGDHG /\
    A != 7 /\ B != 0 /\ C != 8 /\ D != 6 /\
    E != 2 /\ F != 3 /\ G != 4 /\ H != 5;
    
    solve satisfy;
    
    output [ show(ABCD) ++ " + "  ++ show(EFGD) ++ " = " ++ show(FGDHG) ];
    
    % 2465 + 8105 = 10570
    % Finished in 80msec
    

Leave a Comment

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: