Competition #3
This competition is organized by Макарова Наталия (Natalia Makarova)
Definitions
Definition 1:
Magic square is called ultra magic square, if it is both associative (center symmetric) and pandiagonal.
Ultra magic squares exist for orders n > 4.
The Contest
In the contest is required to built ultra magic squares of order 7 – 16 of distinct primes.
Example
n = 5
113 1151 1229 911 101
839 521 41 1013 1091
941 953 701 449 461
311 389 1361 881 563
1301 491 173 251 1289
S=3505
This is the minimal solution for n = 5.
Known as a minimal solution for n = 6 (author M. Alekseyev)
103 59 163 233 139 293
229 257 307 131 13 53
283 17 67 173 181 269
61 149 157 263 313 47
277 317 199 23 73 101
37 191 97 167 271 227
S=990
Rule:
For each order n = 7 – 16 you can imagine several solutions with magic constants S1 <S2 <S3 …
Known solutions:
n = 7, S = 4613 (author N. Makarova)
n = 8, S = 2640 (author N. Makarova)
n = 9, S = 24237 (author A. Chernov)
Contestant shall not be deemed a winner, if he would submit only solutions with known magic constants
Format of solution
The solution is represented in the form:
n: a (1), a (2), a (3), …, a (n^2)
Example:
5:113,1151,1229,911,101,839,521,41,1013,1091,941,953,701,449,461,311,389,1361,881,563,1301,491,173,251,1289
Scoring
Contestant receives for every n the score: Smin/S, where
Smin – the minimal magic constant of solution in the contest;
S – the minimal magic constant of solution by contestant.
The Prize
Winner receives a prize of 3000 rubles.
If the winner is not from Russia, the prize will be paid in $USA at the official rate on the day of end the contest.
Organizers N. Makarova and S. Tognon can participate in the contest, but does not receive the prize in case of winning.