Puzzle
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Ponder This Challenge - November 2019 - Large 9x9 determinant

This month's challenge is from Hugo Pfoertner (thanks!).
Find a 9x9 matrix that contains the digits 1..9, in which each digit appears exactly nine times, whose determinant is at least the hexadecimal number 0x3704d007 (LOOPhOLE upside down in hexadecimal).
A known simple solution uses Latin squares. However, we're looking for solutions that lead to values of the determinant other than those that can be achieved with Latin squares. A bonus '*' will be awarded to the best solution and '**' if you solve the open question of finding a solution that beats the record determinant found with Latin squares.

Solution

  • Oleg Vlasii was the first to solve the open problem and found a non-Latin square with a determinant of 933251220 (=0x37a04894):

    955332288
    492675318
    479218635
    637941825
    628597143
    741829563
    763184952
    186753492
    114466779

    Here is Oleg's solution (thanks!): >>
    And source code of his program: >>

Solvers

  • **Oleg Vlasii (07/11/2019 10:49 PM IDT)
  • Daniel Scheinerman (08/11/2019 08:39 PM IDT)
  • Anders Kaseorg (08/11/2019 10:55 PM IDT)
  • Richard Gosiorovsky (09/11/2019 06:11 PM IDT)
  • Deron Stewart (09/11/2019 11:40 PM IDT)
  • Bert Dobbelaere (11/11/2019 08:30 PM IDT)
  • George Lasry (12/11/2019 03:43 PM IDT)
  • Collin Pearce (12/11/2019 08:45 PM IDT)
  • Benjamin Buhrow (12/11/2019 10:45 PM IDT)
  • Thomas Huet & Eden Saig (14/11/2019 08:51 PM IDT)
  • Daniel Bitin (15/11/2019 03:41 PM IDT)
  • Willem Hendriks (16/11/2019 11:36 PM IDT)
  • Andreas Stiller (17/11/2019 11:09 PM IDT)
  • Thomas Egense (18/11/2019 09:00 AM IDT)
  • Deane Stewart (20/11/2019 06:35 AM IDT)
  • Stéphane Higueret (21/11/2019 06:25 PM IDT)
  • Amos Guler (21/11/2019 08:41 PM IDT)
  • Uoti Urpala (22/11/2019 06:30 AM IDT)
  • David Greer (22/11/2019 08:59 AM IDT)
  • **Andreas Knüpfer (24/11/2019 06:53 PM IDT)
  • Vivek Nema (26/11/2019 08:56 AM IDT)
  • Tom Chen (26/11/2019 03:58 PM IDT)
  • Alper Halbutogullari (26/11/2019 04:10 PM IDT)
  • Omer Shechter & Nir Lavee (28/11/2019 01:35 PM IDT)
  • Lorenz Reichel (30/11/2019 02:01 PM IDT)
  • Albert Stadler (30/11/2019 06:38 PM IDT)
  • **Oscar Volpatti (30/11/2019 10:16 PM IDT)
  • JJ Rabeyrin (30/11/2019 11:26 PM IDT)
  • Radu-Alexandru Todor (01/12/2019 02:19 AM IDT)
  • Bertram Felgenhauer (01/12/2019 02:29 AM IDT)
  • Florian Fischer (01/12/2019 02:56 AM IDT)
  • Li Li (01/12/2019 07:56 AM IDT)

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