August 2019 - Challenge

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This month's challenge is based on a question from Michael Brand. (Thanks!)
Given 9 letters A,B,C,...I , there are 9! = 362,880 different ways to sort them.
Imposing some restrictions, like B>C, C>D, and E>G makes the space smaller (30,240 in this case).

Under a restriction, some of the 36 pairs are determined (B>D, in the example above), and some could be valid in both directions (A>G and G>A are both possible).
In this example we can choose two permutations A<D<C<B<F<G<E<H<I and I<H<G<E<F<D<C<B<A) that cover all the possibilities for the undetermined pairs.
Your challenge, this month, is to find restrictions on 9 letters that is feasible (there exists an order consistent with all restrictions) and no three permutations cover all the pairs.
Supply your answer in the format "B>C, C>D, E>G" and explain why it solves the problem.

Update (12/8): Following many clarification requests, here is an equivalent way of asking the same question:
Remember January 2013's challenge? We asked there to find permutations of N=18 letters that cover all possible orders of K=3 letters.
Asking for all possible orders of pairs (K=2) has a trivial solution. For N=9 it is ABCDEFGHI and IHGFEDCBA.
Our challenge this month is to find constraints on the permutations (E>G means that E must appear after G in each permutation) that will force using at least four permutations to solve (i.e. cover all unrestricted pairs) for K=2 and N=9.

We will post the names of those who submit a correct, original solution! If you don't want your name posted then please include such a statement in your submission!

We invite visitors to our website to submit an elegant solution. Send your submission to the

If you have any problems you think we might enjoy, please send them in. All replies should be sent to:

Challenge: 29/07/2019 @ 12:00 PM EST
Solution: 03/09/2019 @ 12:00 PM EST
List Updated: 04/09/2019 @ 12:00 PM EST

People who answered correctly:

John Tromp (29/07/2019 11:15 AM IDT)
Lorenz Reichel (29/07/2019 02:36 PM IDT)
Thomas Huet (29/07/2019 04:48 PM IDT)
Louis D & Paul M (30/07/2019 12:31 AM IDT)
Jingran Lin (30/07/2019 02:04 AM IDT)
Florian Fischer (30/07/2019 02:08 AM IDT)
Uoti Urpala (30/07/2019 06:42 AM IDT)
Guillaume Escamocher (31/07/2019 06:23 PM IDT)
Vladimir Volevich (31/08/2019 07:23 AM IDT)
Luke Pebody (02/08/2019 01:02 PM IDT)
James Dow Allen (02/08/2019 10:50 PM IDT)
Bert Dobbelaere (04/08/2019 07:01 AM IDT)
Paul Revenant (04/08/2019 07:26 AM IDT)
Jens Leskinen (04/08/2019 04:17 PM IDT)
Alper Halbutogullari (04/08/2019 06:22 PM IDT)
Andreas Stiller (05/08/2019 05:47 PM IDT)
Eden Saig (06/08/2019 02:11 AM IDT)
Louis Faucon (07/08/2019 01:33 AM IDT)
Keith Kaplan (07/08/2019 04:14 AM IDT)
JJ Rabeyrin (07/08/2019 11:37 PM IDT)
Daniel Oliveira (08/08/2019 01:00 AM IDT)
Daniel Bitin (08/08/2019 01:22 PM IDT)
Aaron Zolnai-Lucas (10/08/2019 09:29 PM IDT)
Jacoby Jaeger (12/08/2019 02:11 AM IDT)
Robert Lang (12/08/2019 04:55 PM IDT)
Motty Porat (12/08/2019 11:39 PM IDT)
Chuck Carroll (13/08/2019 02:39 PM IDT)
Arash Yazdani (13/08/2019 10:04 PM IDT)
Todd Will (15/08/2019 11:55 PM IDT)
David Friedman (18/08/2019 04:51 AM IDT)
Kang Jin Cho (20/08/2019 11:24 AM)
Daniel Chong Jyh Tar (26/08/2019 07:45 AM IDT)
David Greer (27/08/2019 12:58 AM IDT)
Daniel Blazewicz (28/08/2019 09:38 AM IDT)
Oscar Volpatti (31/08/2019 04:16 PM IDT)
Vincent Beaud (31-08/2019 11:41 PM IDT)
Radu-Alexandru Todor (01/09/2019 12:24 PM IDT)
Doug Miller (01/09/2019 06:14 AM IDT)
Li Li (01/09/2019 04:38 AM IDT)