Puzzle 1278 A 9x9 Magic square
composed by 81 emirps such that...
On July 24, 2026, Roberto Carlo Angelone sent the
following beautiful nice achievement: a 9x9 Magic
square composed by 81 distinct emirps such that the
associated square is also Magic!... perhps a record
in this subject (who can confirm it?)
|
162742337 |
130317587 |
146344637 |
175384337 |
195157187 |
187664447 |
155565587 |
175058447 |
151864547 |
|
178476737 |
174265877 |
180149687 |
136452647 |
161268377 |
176764037 |
185572217 |
153621257 |
133528277 |
|
161028887 |
168246227 |
131676497 |
136882157 |
168461357 |
164371247 |
160748897 |
193228517 |
195455327 |
|
135688037 |
196231547 |
161897447 |
194311277 |
190347887 |
147372257 |
152259167 |
147526877 |
154464617 |
|
161832227 |
164829317 |
198533057 |
197597027 |
164455457 |
131313887 |
130377857 |
164081597 |
167078687 |
|
174446297 |
181384037 |
176651747 |
181538657 |
138563027 |
134599637 |
167013467 |
132679367 |
193222877 |
|
133455587 |
135682397 |
168162017 |
164539667 |
160449557 |
192028757 |
197234417 |
160664687 |
167882027 |
|
195382637 |
175289657 |
143338697 |
152146877 |
167642537 |
192458267 |
148761227 |
154645037 |
150434177 |
|
177046367 |
153852467 |
173345327 |
141246467 |
133753727 |
153526577 |
182566277 |
198593327 |
166168577 |
&
|
733247261 |
785713031 |
736443641 |
733483571 |
781751591 |
744466781 |
785565551 |
744850571 |
745468151 |
|
737674871 |
778562471 |
786941081 |
746254631 |
773862161 |
730467671 |
712275581 |
752126351 |
772825331 |
|
788820161 |
722642861 |
794676131 |
751288631 |
753164861 |
742173461 |
798847061 |
715822391 |
723554591 |
|
730886531 |
745132691 |
744798161 |
772113491 |
788743091 |
752273741 |
761952251 |
778625741 |
716464451 |
|
722238161 |
713928461 |
750335891 |
720795791 |
754554461 |
788313131 |
758773031 |
795180461 |
786870761 |
|
792644471 |
730483181 |
747156671 |
756835181 |
720365831 |
736995431 |
764310761 |
763976231 |
778222391 |
|
785554331 |
793286531 |
710261861 |
766935461 |
755944061 |
757820291 |
714432791 |
786466061 |
720288761 |
|
736283591 |
756982571 |
796833341 |
778641251 |
735246761 |
762854291 |
722167841 |
730546451 |
771434051 |
|
763640771 |
764258351 |
723543371 |
764642141 |
727357331 |
775625351 |
772665281 |
723395891 |
775861661 |
The Magic sums of both Magic squres are 1480099113 &
6790990149, respectively.
This is the second time that I write a puzzle on
this subject. The first one was in the
Puzzle 165. around the year 2002,
24
years ago! In those years, the best &
only solution I got was the given by an old
puzzler, J. C. Rosa, who got this little pearl:
a 3x3 composed by emirps...: Accoding to my
search never more this Rosa's record was
improved.
|
18544613 |
10175573 |
14646743 |
|
31644581 37557101 34764641 |
|
10557773 |
14455643 |
18353513 |
|
37775501 34655441 31535381 |
|
14264543 |
18735713 |
10366673 |
|
34546241 31753781 37666301 |
Q1. Can you verify the Rosa & Angelone
magic squares?
Q2. Can you produce similar solutions,
nxn magic squares, for n=4, 5, 6, 7 & 8 sizes ?
Q3. Can you get a better matrix than the
Angleone's one, let' say for any n>9?
