Enigmatic Code

Programming Enigma Puzzles

Sphinx Cryptarithm #19

2 Comments Posted by on 11 February 2026

From Sphinx Magazine #142, June 1933

The two words in the name of ROSE–INNES from Yokoama are squares, while OR is a prime number.

What are these numbers?

The puzzle is credited to “M. Pigeolet (Anvers, Belgium)”.

[sphinx19]

sphinx

2 responses to “Sphinx Cryptarithm #19”

  1. Jim Randell's avatarJim Randell 11 February 2026 at 5:05 pm

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

    It runs in 77ms. (Internal runtime of the generated code is 1.5ms).

    #! python3 -m enigma -rr

SubstitutedExpression

"is_square(ROSE)"
"is_square(INNES)"
"is_prime(OR)"

    Solution: ROSE = 9216; INNES = 53361; OR = 29.

    Reply
  2. ruudvanderham's avatarruudvanderham 11 February 2026 at 9:59 pm 
    import peek
import istr

for r, o, s, e in map(tuple, istr.squares(1000, 10000)):
    if (o | r).is_prime() and istr(":=rose").all_distinct():
        for i, n in istr.permutations(set("012345679") - set(rose), 2):
            if istr(":=innes").is_square():
                peek(rose, innes)
    Reply

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