Problems & Puzzles: Puzzles

Puzzle 87.- Adding prime magic squares (a puzzle suggested by John E. Everett)

A.- Let A, B to be two distinct 3x3 prime magic squares. 

This is the least sent as an example by John:

353

167

269

 

277

31

163

 

1

1

1

 

631

199

433

179

263

347

+

43

157

271

+

1

1

1

=

223

421

619

257

359

173

 

151

283

37

 

1

1

1

 

409

643

211

1. Can you find a smaller example than the given above?

B.- Let A, B & C to be 3 distinct 3x3 prime magic squares. Here you are asked to find A, B & C such that A+B+C is another prime magic square.

For this second question I (C.R.) have gotten the following solution

71 461 311   37 547 337   18061 271 9391   18169 1279 10039
521 281 41 + 607 307 7 + 571 9241 17911 = 1699 9829 17959
251 101 491   277 67 577   9091 18211 421   9619 18379 1489

 

2. Can you find a smaller example than the given above?

3.- Redo both exercises for 4x4 prime magic squares

 

Solution

John E. Everett, from Waynesboro, VA, found a smaller example than the mine for question 2.- :

431 59 263   941 29 503   577 103 421   1949 191 1187
83 251 419 + 53 491 929 + 211 367 523 = 347 1109 1871
239 443 71   479 953 41   313 631 157   1031 2027 269

He has also solutions for 3.-, but I'll keep them for a while waiting some solutions from the readers...

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