Puzzle
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Ponder This Challenge - April 2019 - Prime magic square

This month's challenge is from Reda Kebbaj. (Thanks!)

Find nine different prime numbers that can be placed in a 3x3 square in such a way that the average of every row, column, and diagonal is also a prime number.

Solution

  • One can solve for the same prime average for all rows, columns, and diagonals. For example:

     17 89  71
113 59   5
 47 29 101

    Another general solution that also works for larger squares is to find an arithmetic progression of prime numbers and build a regular magic square.

    Lorenz Reichel sent us a solution in which all the secondary diagonals also have prime averages:

    73 43 61
31 79 19
37  7 97

    Jingran Lin found nine different prime numbers that *every* triplet of them averages to a prime number:[440377009, 1109655619, 1206997621, 1371035311, 1778934229, 2448212839, 3117491449, 3786770059, 4456048669]

    Thanks also to Marcelo M De Barros for his blog post on the challenge.

Solvers

  • Adam Daire (27/03/2019 04:23 PM IDT)
  • Daniel Chong Jyh Tar (27/03/2019 04:47 PM IDT)
  • Amos Guler (27/03/2019 05:53 PM IDT)
  • Sanandan Swaminathan (27/03/2019 06:29 PM IDT)
  • Kevin Bauer (27/03/2019 06:38 PM IDT)
  • JJ Rabeyrin (27/03/2019 10:35 PM IDT)
  • Lorenz Reichel (27/03/2019 11:32 PM IDT)
  • Alper Halbutogullari (27/03/2019 11:43 PM IDT)
  • Bert Dobbelaere (27/03/2019 11:46 PM IDT)
  • Eden Saig (28/03/2019 01:14 AM IDT)
  • Bryce Fore (28/03/2019 01:26 AM IDT)
  • Anders Kaseorg (28/03/2019 05:20 AM IDT)
  • Graham Hemsley (28/03/2019 11:47 AM IDT)
  • Joaquim Neves Carrapa (28/03/2019 11:54 AM IDT)
  • Uoti Urpala (28/03/2019 12:06 PM IDT)
  • Xiao Liu (28/03/2019 02:14 PM IDT)
  • Robert Lang (28/03/2019 04:10 PM IDT)
  • Alex Fleischer (28/03/2019 06:01 PM IDT)
  • Evert van Dijken (28/03/2019 07:04 PM IDT)
  • Oscar Volpatti (28/03/2019 08:16 PM IDT)
  • Deniz Yuret (28/03/2019 09:44 PM IDT)
  • Todd Will (28/03/2019 11:29 PM IDT)
  • Hugo Pfoertner (28/03/2019 11:40 PM IDT)
  • Chuck Carroll (28/03/2019 11:44 PM IDT)
  • Haye Chan (29/03/2019 03:05 AM IDT)
  • Gary M. Gerken (29/03/2019 04:45 AM IDT)
  • Dan Dima (29/03/2019 10:47 AM IDT)
  • Armin Krauß (29/03/2019 12:55 PM IDT)
  • Harald Bögeholz (29/03/2019 03:42 PM IDT)
  • Sergey Coolcat (29/03/2019 03:08 PM IDT)
  • Matthew Charlap (29/03/2019 04:53 PM IDT)
  • Guillaume Escamocher (29/03/2019 06:49 PM IDT)
  • Alexander Daryin (29/03/2019 08:09 PM IDT)
  • Kai Guttmann (29/03/2019 09:47 PM IDT)
  • Rashid Naimi (30/03/2019 01:48 AM IDT)
  • Marco Bellocchi (30/03/2019 02:06 AM IDT)
  • Mehmet Saruhan (30/03/2019 02:37 AM IDT)
  • Pål Hermunn Johansen (30/03/2019 03:20 AM IDT)
  • Andreas Stiller (30/03/2019 05:29 AM IDT)
  • Clive Tong (30/03/2019 10:18 AM IDT)
  • Richard Gosiorovsky (30/03/2019 12:22 PM IDT)
  • Philippe Fondanaiche (30/03/2019 01:03 PM IDT)
  • Noam & Ayal Zaks (30/03/2019 01:54 PM IDT)
  • Michael Liepelt (30/03/2019 02:35 PM IDT)
  • Thomas Huet (30/03/2019 05:19 PM IDT)
  • Paul Revenant (30/03/2019 09:36 PM IDT)
  • Florian Fischer (30/03/2019 11:24 PM IDT)
  • Boaz Menuhin (31/03/2019 01:08 AM IDT)
  • Raymond Lo (31/03/2019 09:01 AM IDT)
  • Kang Jin Cho (31/03/2019 12:01 PM IDT)
  • Thomas Egense (31/03/2019 12:58 PM IDT)
  • Anson Ho (31/03/2019 01:05 PM IDT)
  • Vladimir M. Milovanović (01/04/2019 02:12 AM IDT)
  • Prashant Wankhede (01/04/2019 03:49 AM IDT)
  • Frank Schoeps (01/04/2019 05:16 AM IDT)
  • Tom Chen (01/04/2019 06:12 AM IDT)
  • David F.H. Dunkley (31/03/2019 07:08 PM IDT)
  • Walter Schmidt (01/04/2019 08:25 AM IDT)
  • Shouky Dan & Tamir Ganor (01/04/2019 11:23 AM IDT)
  • Rudy Cortembert (01/04/2019 11:46 AM IDT)
  • Brett Grothouse (01/04/2019 11:54 AM IDT)
  • Reiner Martin (01/04/2019 12:42 PM IDT)
  • Christian Pfaffenzeller (01/04/2019 04:41 PM IDT)
  • Charles Joscelyne (01/04/2019 04:51 PM IDT)
  • Vanio Beccaccioli (02/04/2019 12:10 AM IDT)
  • Rick Kaye (02/04/2019 02:46 AM IDT)
  • Alan Murray (02/04/2019 03:52 AM IDT)
  • Gumpina Rama Krishna Chaitanya (02/04/2019 06:08 AM IDT)
  • Johnathon Shook (02/04/2019 08:01 AM IDT)
  • Anunay Kulshrestha (02/04/2019 09:03 AM IDT)
  • Dieter Beckerle (02/04/2019 10:07 AM IDT)
  • K.S.G. Sarma (02/04/2019 03:38 AM IDT)
  • Yash Patil (02/04/2019 06:36 PM IDT)
  • Cameron Byer (02/04/2019 06:52 PM IDT)
  • Yash Pote (02/04/2019 10:54 PM IDT)
  • Muharrem Gorkem (03/04/2019 12:12 AM IDT)
  • Caili Shen (03/04/2019 12:32 AM IDT)
  • Jordan Rinder (03/04/2019 01:49 AM IDT)
  • You Soon Ho (03/04/2019 10:27 AM IDT)
  • Nguyen Khac Tung (03/04/2019 01:16 PM IDT)
  • Kandala Viswakanth (03/04/2019 03:39 PM IDT)
  • Benjamin Buhrow (03/04/2019 04:42 PM IDT)
  • Franciraldo Cavalcante (03/04/2019 05:07 PM IDT)
  • Rogerio Ponce da Silva (03/04/2019 06:00 PM IDT)
  • Luke Richards (03/04/2019 06:09 PM IDT)
  • Latchezar Christov (03/04/2019 08:14 PM IDT)
  • Kandala Srinivas (03/04/2019 08:26 PM IDT)
  • Wayne Petrychyn (03/04/2019 08:38 PM IDT)
  • Deron Stewart (03/04/2019 10:55 PM IDT)
  • Phil Benamy (04/04/2019 02:48 AM IDT)
  • Hannah Leaman (04/04/2019 03:21 AM IDT)
  • Yuanjie Pu (04/04/2019 07:11 AM IDT)
  • Hayk Aleksanyan (04/04/2019 09:39 AM IDT)
  • Rustam Salikhov (04/04/2019 10:12 AM IDT)
  • Aditya Dalal (04/04/2019 01:56 PM IDT)
  • Vladimir Volevich (04/04/2019 03:05 PM IDT)
  • Dominik Reichl (04/04/2019 05:32 PM IDT)
  • Peter Gerritson (04/04/2019 09:13 PM IDT)
  • Paul McKenney (04/04/2019 0921:46 PM IDT)
  • Michael Rosola (04/04/2019 11:48 PM IDT)
  • Rainer Rosenthal (05/04/2019 01:16 AM IDT)
  • Spencer Ong (05/04/2019 12:58 PM IDT)
  • Daniel Bitin (05/04/2019 01:38 PM IDT)
  • Mantha Bharadwaj (05/04/2019 01:52 PM IDT)
  • Seth Cohen (05/04/2019 02:44 PM IDT)
  • Kipp Johnson (05/04/2019 04:35 PM IDT)
  • Yuxuan Shui (05/04/2019 05:53 PM IDT)
  • Kkm Sarma (05/04/2019 10:41 PM IDT)
  • Soumitra Agarwal (06/04/2019 06:08 AM IDT)
  • David Friedman (07/04/2019 07:40 AM IDT)
  • Mauro Bampo (07/04/2019 03:28 PM IDT)
  • Min Jung Kim (07/04/2019 04:36 PM IDT)
  • Jeewoo Lee (07/04/2019 05:24 PM IDT)
  • Fabio Michele Negroni (07/04/2019 05:47 PM IDT)
  • Marcelo De Barros (08/04/2019 01:41 AM IDT)
  • Jonas Beachy (08/04/2019 01:56 AM IDT)
  • Francisco Couzo (08/04/2019 03:06 AM IDT)
  • Serge Batalov (08/04/2019 03:56 AM IDT)
  • Bharat Kumar Aryasomayajula (07:12 AM IDT)
  • Ulf Brännlund (08/04/2019 09:21 AM IDT)
  • Kenneth Kwok (08/04/2019 10:37 AM IDT)
  • Rajesh Sathiyanarayanan (08/04/2019 11:21 AM IDT)
  • Vivek Nema (08/04/2019 05:14 PM IDT)
  • Maximilian Maczasek (08/04/2019 09:13 PM IDT)
  • Yasodhar Patnaik (08/04/2019 10:58 PM IDT)
  • Greg Janée (09/04/2019 07:15 PM IDT)
  • David Keyes (10/04/2019 01:49 AM IDT)
  • Fabio Filatrella (11/04/2019 11:41 AM IDT)
  • Harold Gutch (11/04/2019 11:45 AM IDT)
  • Sebastian Bohm & Martí Bosch (11/04/2019 01:08 PM IDT)
  • Dario Filatrella (11/04/2019 06:30 PM IDT)
  • Hanlin Ren (12/04/2019 08:10 AM IDT)
  • Andrejs Pilka (12/04/2019 01:40 PM IDT)
  • Nigel Brumpton (12/04/2019 06:51 PM IDT)
  • Barry O’Sullivan (13/04/2019 01:48 AM IDT)
  • Ryan Riley (13/04/2019 09:53 AM IDT)
  • David Greer (13/04/2019 10:46 PM IDT)
  • Fakih Karademir (14/04/2019 12:15 PM IDT)
  • Boris Silantyev (14/04/2019 01:57 PM IDT)
  • Eoin Kenny (14/04/2019 02:54 PM IDT)
  • Yi Won Kim (14/04/2019 05:10 PM IDT)
  • Almog Yair (14/04/2019 10:44 PM IDT)
  • Joseph DeVincentis (15/04/2019 17:28 PM IDT)
  • Andreas Knüpfer (15/04/2019 10:28 PM IDT)
  • Maksym Voznyy (16/04/2019 05:51 AM IDT)
  • Low Choo Ray (16/04/2019 08:52 AM IDT)
  • Misha Lavrov (16/04/2019 11:21 PM IDT)
  • Jingran Lin (17/04/2019 01:17 AM IDT)
  • Tom Sirgedas (17/04/2019 01:48 AM IDT)
  • Ignat Soroko (17/04/2019 11:12 AM IDT)
  • Hamidreza Bidar (18/04/2019 03:04 PM IDT)
  • Mikhail Berezovskiy (20/04/2019 07:22 AM IDT)
  • Cheng Xizhe (20/04/2019 03:04 PM IDT)
  • Hakan Summakoğlu (20/04/2019 06:11 PM IDT)
  • Joonsoo Lee (20/04/2019 07:20 PM IDT)
  • Shail Patel (21/04/2019 02:20 AM IDT)
  • Andrew Lee (21/04/2019 04:33 PM IDT)
  • Jiho Lee (21/04/2019 05:22 PM IDT)
  • Hashimoto Ryuichi (22/04/2019 08:08 AM IDT)
  • Motty Porat (22/04/2019 09:57 PM IDT)
  • Vladimir Dorofeev (23/04/2019 02:58 PM IDT)
  • Erik Hostens (23/04/2019 04:42 PM IDT)
  • Philip Grabowski (23/04/2019 10:23 PM IDT)
  • Hannes Schenck (23/04/2019 11:15 PM IDT)
  • Hao Zheng (24/04/2019 12:05 AM IDT)
  • Walter Sebastian Gisler (24/04/2019 12:17 PM IDT)
  • Erik Wünstel (24/04/2019 12:49 PM IDT)
  • Ismail Bozkurt (25/04/2019 01:46 AM IDT)
  • Muhammed Halbutogullari (25/04/2019 06:27 AM IDT)
  • Steven Langerwerf (25/04/2019 06:00 PM IDT)
  • Alexey Zyl (26/04/2019 03:22 PM IDT)
  • Eric Edward Pauley (26/04/2019 07:55 PM IDT)
  • Jason Ke (27/04/2019 01:49 AM IDT)
  • Arnab Moitra (27/04/2019 12:39 PM IDT)
  • Feyzullah Egriboyun (27/04/2019 02:08 PM IDT)
  • Kelvin Kim (27/04/2019 06:27 PM IDT)
  • Samhita Madduri (28/04/2019 05:34 AM IDT)
  • Andrea Andenna (28/04/2019 12:30 PM IDT)
  • Andras Varga (29/04/2019 12:24 PM IDT)
  • Tilo Anschütz (29/04/2019 01:42 PM IDT)
  • Ralf Jonas (29/04/2019 04:29 PM IDT)
  • Jun Sakai (29/04/2019 05:34 PM IDT)
  • Michael J. Swart (29/04/2019 11:58 PM IDT)
  • Elizabeth Harper (30/04/2019 12:04 AM IDT)
  • Stefan Wirth (30/04/2019 02:04 AM IDT)
  • Daniëlle van den Berg (30/04/2019 04:30 PM IDT)
  • Radu-Alexandru Todor (30/04/2019 09:08 PM IDT)

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