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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