IXOHOXI (and up-site-down) magic square
Why using sequencial numbers in the magic square? See how you can use digits presented like this 
and if you put the magic square up-site down or you mirror the magic square horizontally or vertically you get another valid magic square. That
is called a (real) IXOHOXI magic square.
The up-site-down magic square (with e.g. the digits 6 and 9) cannot be mirrored.
Original of the IXOHOXI magic square
|
|
|
19998 |
19998 |
19998 |
19998 |
|
|
|
19998 |
|
|
|
|
19998 |
|
19998 |
|
8818 |
1111 |
8188 |
1881 |
|
|
19998 |
|
8181 |
1888 |
8811 |
1118 |
|
|
19998 |
|
1811 |
8118 |
1181 |
8888 |
|
|
19998 |
|
1188 |
8881 |
1818 |
8111 |
|
IXOHOXI magic square up-site down
|
|
|
19998 |
19998 |
19998 |
19998 |
|
|
|
19998 |
|
|
|
|
19998 |
|
19998 |
|
1118 |
8181 |
1888 |
8811 |
|
|
19998 |
|
8888 |
1811 |
8118 |
1181 |
|
|
19998 |
|
8111 |
1188 |
8881 |
1818 |
|
|
19998 |
|
1881 |
8818 |
1111 |
8188 |
|
IXOHOXI magic square horizontally mirrored
|
|
|
19998 |
19998 |
19998 |
19998 |
|
|
|
19998 |
|
|
|
|
19998 |
|
19998 |
|
1881 |
8818 |
1111 |
8188 |
|
|
19998 |
|
8111 |
1188 |
8881 |
1818 |
|
|
19998 |
|
8888 |
1811 |
8118 |
1181 |
|
|
19998 |
|
1118 |
8181 |
1888 |
8811 |
|
IXOHOXI magic square vertically mirrored
|
|
|
19998 |
19998 |
19998 |
19998 |
|
|
|
19998 |
|
|
|
|
19998 |
|
19998 |
|
1188 |
8881 |
1818 |
8111 |
|
|
19998 |
|
1811 |
8118 |
1181 |
8888 |
|
|
19998 |
|
8181 |
1888 |
8811 |
1118 |
|
|
19998 |
|
8818 |
1111 |
8188 |
1881 |
|
Source: Magic square lexicon, H.D. Heinz & J.R. Hendricks
Original up-site-down magic square (ignore comma)
|
|
|
264 |
264 |
264 |
264 |
264 |
|
|
|
|
|
264 |
|
|
|
|
|
264 |
|
|
|
264 |
|
0,0 |
1,1 |
6,6 |
8,8 |
9,9 |
|
|
|
|
264 |
|
8,6 |
9,8 |
0,9 |
1,0 |
6,1 |
|
264 |
264 |
|
264 |
|
1,9 |
6,0 |
8,1 |
9,6 |
0,8 |
|
264 |
264 |
|
264 |
|
9,1 |
0,6 |
1,8 |
6,9 |
8,0 |
|
264 |
264 |
|
264 |
|
6,8 |
8,9 |
9,0 |
0,1 |
1,6 |
|
264 |
264 |
Magic square up-site down
|
|
|
264 |
264 |
264 |
264 |
264 |
|
|
|
|
|
264 |
|
|
|
|
|
264 |
|
|
|
264 |
|
9,1 |
1,0 |
0,6 |
6,8 |
8,9 |
|
|
|
|
264 |
|
0,8 |
6,9 |
8,1 |
9,0 |
1,6 |
|
264 |
264 |
|
264 |
|
8,0 |
9,6 |
1,8 |
0,9 |
6,1 |
|
264 |
264 |
|
264 |
|
1,9 |
0,1 |
6,0 |
8,6 |
9,8 |
|
264 |
264 |
|
264 |
|
6,6 |
8,8 |
9,9 |
1,1 |
0,0 |
|
264 |
264 |
Source: Mr. Collison's order 5 pandiagonal upsite-down magic square
Original of the IXOHOXI magic square
|
|
|
3111108 |
3111108 |
3111108 |
3111108 |
3111108 |
3111108 |
3111108 |
3111108 |
|
|
|
|
|
3111108 |
|
|
|
|
|
|
|
|
3111108 |
|
|
|
3111108 |
|
225555 |
525222 |
522255 |
222522 |
255252 |
555525 |
552552 |
252225 |
|
|
|
|
3111108 |
|
255225 |
555552 |
552525 |
252252 |
225522 |
525255 |
522222 |
222555 |
|
3111108 |
3111108 |
|
3111108 |
|
222222 |
522555 |
525522 |
225255 |
252525 |
552252 |
555225 |
255552 |
|
3111108 |
3111108 |
|
3111108 |
|
252552 |
552225 |
555252 |
255525 |
222255 |
522522 |
525555 |
225222 |
|
3111108 |
3111108 |
|
3111108 |
|
522525 |
222252 |
225225 |
525552 |
552222 |
252555 |
255522 |
555255 |
|
3111108 |
3111108 |
|
3111108 |
|
552255 |
252522 |
255555 |
555222 |
522552 |
222225 |
225252 |
525525 |
|
3111108 |
3111108 |
|
3111108 |
|
525252 |
225525 |
222552 |
522225 |
555555 |
255222 |
252255 |
552522 |
|
3111108 |
3111108 |
|
3111108 |
|
555522 |
255255 |
252222 |
552555 |
525225 |
225552 |
222525 |
522252 |
|
3111108 |
3111108 |
IXOHOXI magic square up-site down (2 becomes 5 and 5 becomes 2)
|
|
|
3111108 |
3111108 |
3111108 |
3111108 |
3111108 |
3111108 |
3111108 |
3111108 |
|
|
|
|
|
3111108 |
|
|
|
|
|
|
|
|
3111108 |
|
|
|
3111108 |
|
525552 |
252555 |
522255 |
255252 |
222522 |
555525 |
225225 |
552222 |
|
|
|
|
3111108 |
|
552522 |
225525 |
555225 |
222222 |
255552 |
522555 |
252255 |
525252 |
|
3111108 |
3111108 |
|
3111108 |
|
252252 |
525255 |
255555 |
522552 |
555222 |
222225 |
552525 |
225522 |
|
3111108 |
3111108 |
|
3111108 |
|
225222 |
552225 |
222525 |
555522 |
522252 |
255255 |
525555 |
252552 |
|
3111108 |
3111108 |
|
3111108 |
|
555255 |
222252 |
552552 |
225555 |
252225 |
525222 |
255522 |
522525 |
|
3111108 |
3111108 |
|
3111108 |
|
522225 |
255222 |
525522 |
252525 |
225255 |
552252 |
222552 |
555555 |
|
3111108 |
3111108 |
|
3111108 |
|
222555 |
555552 |
225252 |
552255 |
525525 |
252522 |
522222 |
255225 |
|
3111108 |
3111108 |
|
3111108 |
|
255525 |
522522 |
252222 |
525225 |
552555 |
225552 |
555252 |
222255 |
|
3111108 |
3111108 |
IXOHOXI magic square horizontally mirrored (2 becomes 5 and 5 becomes 2)
|
|
|
3111108 |
3111108 |
3111108 |
3111108 |
3111108 |
3111108 |
3111108 |
3111108 |
|
|
|
|
|
3111108 |
|
|
|
|
|
|
|
|
3111108 |
|
|
|
3111108 |
|
255525 |
522522 |
252222 |
525225 |
552555 |
225552 |
555252 |
222255 |
|
|
|
|
3111108 |
|
222555 |
555552 |
225252 |
552255 |
525525 |
252522 |
522222 |
255225 |
|
3111108 |
3111108 |
|
3111108 |
|
522225 |
255222 |
525522 |
252525 |
225255 |
552252 |
222552 |
555555 |
|
3111108 |
3111108 |
|
3111108 |
|
555255 |
222252 |
552552 |
225555 |
252225 |
525222 |
255522 |
522525 |
|
3111108 |
3111108 |
|
3111108 |
|
225222 |
552225 |
222525 |
555522 |
522252 |
255255 |
525555 |
252552 |
|
3111108 |
3111108 |
|
3111108 |
|
252252 |
525255 |
255555 |
522552 |
555222 |
222225 |
552525 |
225522 |
|
3111108 |
3111108 |
|
3111108 |
|
552522 |
225525 |
555225 |
222222 |
255552 |
522555 |
252255 |
525252 |
|
3111108 |
3111108 |
|
3111108 |
|
525552 |
252555 |
522255 |
255252 |
222522 |
555525 |
225225 |
552222 |
|
3111108 |
3111108 |
IXOHOXI magic square vertically mirrored (2 becomes 5 and 5 becomes 2)
|
|
|
3111108 |
3111108 |
3111108 |
3111108 |
3111108 |
3111108 |
3111108 |
3111108 |
|
|
|
|
|
3111108 |
|
|
|
|
|
|
|
|
3111108 |
|
|
|
3111108 |
|
222255 |
522522 |
525555 |
225222 |
252552 |
552225 |
555252 |
255525 |
|
|
|
|
3111108 |
|
252525 |
552252 |
555225 |
255552 |
222222 |
522555 |
525522 |
225255 |
|
3111108 |
3111108 |
|
3111108 |
|
225522 |
525255 |
522222 |
222555 |
255225 |
555552 |
552525 |
252252 |
|
3111108 |
3111108 |
|
3111108 |
|
255252 |
555525 |
552552 |
252225 |
225555 |
525222 |
522255 |
222522 |
|
3111108 |
3111108 |
|
3111108 |
|
525225 |
225552 |
222525 |
522252 |
555522 |
255255 |
252222 |
552555 |
|
3111108 |
3111108 |
|
3111108 |
|
555555 |
255222 |
252255 |
552522 |
525252 |
225525 |
222552 |
522225 |
|
3111108 |
3111108 |
|
3111108 |
|
522552 |
222225 |
225252 |
525525 |
552255 |
252522 |
255555 |
555222 |
|
3111108 |
3111108 |
|
3111108 |
|
552222 |
252555 |
255522 |
555255 |
522525 |
222252 |
225225 |
525552 |
|
3111108 |
3111108 |
This IXOHOXI square is bimagic as well!!!
Bron: Professor Inder Jeet Taneja, oktober 2010
Professor Inder Jeet Taneja (Departamento de Matemática, Universidade Federal de Santa Catarina, 88.040-900 Florianópolis, SC, Brazil) produced a lot of awesome IXOHOXI (bi)magic squares of different orders and with different combinations of digits.
