Enigmatic Code

Programming Enigma Puzzles

Enigma 528: An enigma for U

From New Scientist #1680, 2nd September 1989 [link]

Here are just three rows from our local football league table at the end of the season, after each team in the league has played each of the others once. The teams have been put in alphabetical order here.

Enigma 528

There are three points for a win and one for a draw and, in the table, digits have been consistently replaced by letters with different letters used for different digits.

Please find AGAIN. And tell me who (if anybody) won when City played Albion.


It’s the 8th anniversary of Enigmatic Code, and this puzzle brings the total number of Enigma puzzles posted to 1335, which is 75% of the 1780 Enigma puzzles published in New Scientist. There is a complete archive of puzzles from the first Enigma puzzle in February 1979 up to September 1989, and also from June 1998 up to the final Enigma puzzle in December 2013. There are 457 Enigma puzzles remaining to post.

Also available are puzzles from the Puzzle series, which were published in New Scientist before Enigma started. There is a complete archive available from July 1977 until the end of the Puzzle series in February 1979 (83 puzzles). There are 7 puzzles in this series remaining to post.

And before that was the Tantalizer series of puzzles, of which there is a complete archive from September 1975 up to the end of the Tantalizer series in May 1977 (84 puzzles).

Earlier in 2019 New Scientist started publishing a new series of puzzles (the “Puzzle #” series), and I have been posting these to the site, along with my notes, as they became available.

I have also been posting my notes on Sunday Times Teaser puzzles at the S2T2 site, and there are currently 227 puzzles available there.

So between the two sites there are currently 1766 puzzles available, which is almost the total number of Enigma puzzles published.


One response to “Enigma 528: An enigma for U

  1. Jim Randell 2 December 2019 at 9:45 am

    We can generate a collection of constraints that can be solved using the [[ SubstitutedExpression() ]] solver from the enigma.py library.

    The following run file executes in 135ms.

    Run: [ @repl.it ]

    #!/usr/bin/env python -m enigma -r
    # City.points
    "3 * G + M = EN"
    # City.played
    "G + M + A = I"
    # City.goals_for
    "U > G"
    # Albion.points
    "AN <= 3 * I"
    # Town.won, Town.lost
    "X + X <= I"
    # required answer

    From the output of the program we see:

    Albion: Points = 25
    City: Played = 9, Won = 4, Drawn = 3, Lost = 2, Points = 15
    Town: Won = 0, Lost = 0

    So each team has played 9 matches (i.e. there must be 10 teams altogether). And Town must have drawn all their matches. Albion has 25 points, which can only have come from 8 wins and 1 draw. The 1 draw must be the Albion vs. Town match, so Albion must have won the Albion vs. City match.

    Solution: AGAIN = 24295. Albion beat City.

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