Problems & Puzzles: Puzzles

Puzzle 867. Follow up to Puzzle 833. Q. Redo Puzzle 833 but generating solutions for a matrix Rx4, S is minimal and prime, for R=3 to 10.

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Contribution came from Emmanuel Vantieghem

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Emmanuel wrote:

Here is what I could find about puzzle 867 :
 

S, R, P :
 

23, 2, 480

31, 3, 1680

41, 4, 1890

47, 5, 3360

67, 6, 15120

71, 7, 30240

97, 8, 60480

101, 9, 60480

109, 10, 181440

113, 11, 181440

167, 12, 604800

173, 13, 665280

181, 15, 1330560

227, 16, 1995840

233, 17, 1663200

257, 18, 3991680

311, 21, 5987520

337, 24, 6652800

347, 24, 25945920

359, 25, 7983360

421, 28, 29937600

461, 30, 25945920

503, 31, 103783680

541, 33, 51891840

557, 34, 86486400

619, 39, 129729600

701, 42, 259459200

823, 43, 389188800

853, 46, 778377600

907, 47, 518918400

997, 50, 908107200

1087, 52, 648648000

1109, 56, 778377600

1213, 57, 1816214400

1373, 61, 4410806400
 

For instance, here are the 21 solutions of the equation  x+y+z+t = 311  and  xyzt = 5987520 :

{6, 77, 108, 120}

{6, 80, 99, 126}

{8, 45, 126, 132}

{8, 54, 84, 165}

{9, 40, 108, 154}

{9, 44, 90, 168}

{9, 56, 66, 180}

{11, 30, 126, 144}

{11, 36, 84, 180}

{11, 45, 63, 192}

{12, 27, 132, 140}

{12, 45, 56, 198}

{14, 24, 108, 165}

{15, 22, 112, 162}

{15, 27, 77, 192}

{16, 27, 70, 198}

{20, 21, 72, 198}

{20, 33, 42, 216}

{21, 30, 44, 216}

{22, 28, 45, 216}

{27, 28, 36, 220}

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