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.

Contribution came from Emmanuel Vantieghem

***

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}

***

 Records   |  Conjectures  |  Problems  |  Puzzles