Bimagic Square of Order 23

Jacques Guéron

Original Bimagic Square of Order 23. By @ Jacques Guéron, 2006. Second Original Bimagic Square of same order 23 by @ Mikael Hermansson, November 2021. S2=2151535.

Biography of Jacques Guéron:

Jacques Guéron (Nice 1948 -) Photo in his office, taken by his wife in February 2006. Click on the image to enlarge it (541KB). I am 57 years old and I am passionate about magic squares; I think I got a taste for it from the age of 12 or 13. My first computer in 1985: an Amstrad CPC 64 monochrome screen and cassettes! It allowed me, thanks to the Basic language, to progress quickly in the development of magic squares although I had already constructed many of them by hand (in 1982-83 for example by hand a magic 64x64 of which 2 consecutive squares are precisely 1982-1983, which is of course not a new idea). I have had quite a few books on magic squares for a long time. With the web and in particular www.multimagie.com run by Mr. Christian Boyer, I am overwhelmed with information on this subject. I am also passionate about magical horse riding circuits; passion prior to multimagic but now surpassed by the latter! Today, I work with a Pentium 4 clocked at 2.8 GHz and with the Pascal language through Delphi 5. But I must admit that when it comes to magic squares (multimagic), the brute force of a computer is far to be sufficient: as I mentioned above, passion is essential. Then, as there is no real law for the general construction of magic squares, you need a good dose of imagination and patience to find tips so as not to get lost in calculations that are impossible to carry out in time but also I had to familiarize myself with Pascal, which I learned on the job; in fact my training is rather mathematical, it certainly helped me a lot with magic squares in the field of combinatorial analysis. I have an atypical curriculum: with a baccalaureate C, a first year of Maths Physics (in the computer science part we learned Algol at the time, which is obsolete today), a D.U.T in Electrical Engineering I became a professor of Mathematics through cooperation in Morocco and in different private schools in France; It was only at the age of 48 that I obtained my degree in Maths, which I prepared through distance learning courses at the University of Provence. From there, I was able to teach under contract as an auxiliary teacher with the diocese (still faithful to the private sector having done my Terminale C myself in Vichy at the Saint Dominique college). I have taught at all levels from middle and high school to Terminale, BEP, BTS accounting and IT, but what I appreciate most today are my private lessons with Terminale S, ES students. and even first year of Deug with whom a discussion on magic squares is always easier than in the noisy and often undisciplined classes of our days; in any case I have hope to imagine in conclusion and thinking of the computer science student (Fredrik Jansson with his first bimagic of order 10 in 2004) as well as the popularity of multimagie.com that magic squares will become a real mathematical recreation increasingly popular with younger generations. In the Excel file of my bimagic square of 13, without revealing all my secrets, there is truly my way of acting for future bimagic squares and in particular on the bimagic of 17 currently under construction! Jacques Guéron February 24, 2006

Notes from Christian Boyer:

Just a few days after this biography, Jacques Guéron actually succeeded in constructing the first bimagic squares of order 17 then 19! As for his order 13 bimagic, the secrets of constructing his order 19 bimagics are in his Excel file downloadable from the site. www.multimagie.com / translated with google language translator 2023-10-01 by Mikael Hermansson

001	045	466	089	490	133	390	177	408	221	301	265	034	517	245	355	109	203	284	347	202	523	290
049	512	281	340	051	274	099	492	176	499	220	461	243	296	216	077	500	167	074	159	299	444	166
095	186	235	482	237	228	273	456	055	474	036	357	080	484	153	201	168	064	303	506	259	505	258
187	396	189	486	145	006	409	388	317	402	057	504	263	302	420	108	315	487	119	244	025	256	070
419	278	143	416	097	182	181	432	101	384	149	150	401	033	524	454	210	250	163	522	116	073	417
141	232	331	448	191	352	365	192	435	102	343	376	447	332	032	392	030	439	028	407	069	385	026
443	140	093	236	411	052	345	100	147	358	453	394	493	125	383	375	330	029	111	067	429	423	158
184	363	090	367	042	333	132	510	491	148	515	458	151	171	199	062	346	213	446	338	071	114	351
412	341	048	511	178	529	300	039	371	056	195	311	342	255	078	154	251	350	502	442	115	247	068
230	321	044	399	480	313	234	307	222	288	082	242	426	217	295	498	155	018	208	072	496	022	526
233	094	003	282	283	098	227	146	238	507	103	289	525	459	061	123	292	527	382	377	381	353	112
276	275	272	271	270	489	053	269	268	267	414	520	477	060	264	031	017	254	334	020	483	118	393
372	445	226	387	318	441	280	231	286	194	241	196	013	152	309	521	076	479	019	027	348	066	468
322	229	508	225	224	469	188	131	009	310	277	104	059	360	501	428	063	437	473	297	249	209	023
324	463	136	190	335	185	007	395	193	129	386	035	291	433	015	214	370	380	519	305	021	465	304
361	183	359	179	362	421	040	364	130	037	472	424	218	079	124	262	422	121	065	162	513	294	503
138	091	450	139	088	239	142	285	518	427	488	081	126	478	107	246	205	110	398	425	400	397	117
092	137	410	096	134	413	434	054	323	083	011	058	197	373	476	329	405	298	430	470	157	337	378
516	431	436	320	005	087	086	344	462	175	174	173	369	014	354	475	449	156	253	113	328	160	215
279	389	391	135	374	379	464	008	368	010	128	339	314	403	170	016	122	308	356	206	452	024	460
481	047	180	043	514	144	509	223	038	457	418	127	349	198	325	169	471	075	207	257	211	316	336
494	495	319	050	451	041	497	085	455	327	266	012	172	106	406	312	261	404	161	212	165	200	204
046	002	485	004	415	287	440	467	084	240	366	219	105	248	438	293	528	326	260	120	306	164	252

018	481	190	249	256	479	038	431	031	354	310	069	287	314	234	030	453	456	363	231	371	364	086
485	529	441	064	397	040	353	140	309	122	229	265	496	285	013	421	175	246	327	328	183	240	007
134	343	044	341	524	385	142	121	128	213	473	026	267	110	228	215	422	411	043	505	286	460	274
344	435	048	395	302	293	074	257	056	475	494	173	450	377	046	362	329	227	466	271	024	272	025
298	389	082	199	178	339	338	165	428	095	187	154	083	498	198	500	138	502	091	461	123	504	145
252	111	114	387	348	433	098	349	146	429	381	380	129	006	497	320	076	367	280	414	008	113	457
167	346	163	440	197	488	020	398	382	039	015	072	379	331	359	184	468	084	317	459	192	179	416
390	087	294	437	478	119	430	185	172	383	077	136	037	147	405	200	155	419	501	101	463	372	107
209	300	131	486	217	050	223	296	242	308	448	288	104	235	313	375	032	322	512	034	458	004	508
189	118	019	482	001	352	491	230	474	159	335	219	188	452	275	279	376	028	180	415	088	462	283
436	297	248	527	432	247	384	303	023	292	427	241	005	469	071	238	407	148	003	149	153	418	177
255	254	259	258	041	260	261	477	263	262	116	010	053	266	470	513	499	196	276	047	510	137	412
085	158	143	304	089	212	299	250	336	244	289	334	517	221	378	454	009	511	051	182	503	062	464
067	206	340	394	345	195	135	523	401	337	144	495	239	515	097	160	316	011	150	509	225	226	065
301	208	305	022	061	306	399	342	220	521	253	426	471	029	170	467	102	057	093	281	233	507	321
439	392	391	080	291	442	245	388	103	012	042	449	404	423	052	325	284	132	420	130	105	413	133
347	169	351	171	109	168	166	490	493	400	058	106	312	406	451	108	268	465	409	017	368	027	236
099	014	210	094	443	525	186	444	355	068	356	357	161	176	516	081	055	277	374	202	417	315	370
393	438	434	120	117	396	476	096	447	207	519	472	333	054	157	125	201	100	232	373	060	152	193
483	049	487	350	386	016	307	021	073	492	112	403	181	205	332	059	361	323	455	319	273	194	214
141	251	395	139	151	156	522	066	520	162	402	191	216	360	127	408	514	174	222	078	324	070	506
528	484	526	045	243	115	063	090	290	446	164	311	425	092	282	002	237	270	204	224	410	278	366
035	036	480	211	486	079	445	033	203	075	264	518	358	124	424	269	218	369	126	365	318	326	330

Micke