TABLE-2
SUM of 3 numbers (1) | no. of combination--without repetition ; triplets- [a,b,c] | no. of combinations --with repetition (cb) lets-[a,b,c] |
03 | 0 | 1(1,1,1) |
04 | 0 | 1(1,1,2) |
05 | 0 | 2(1,1,3)(2,2,1) |
06 | 1(1,2,3) | 2(2,2,2)(1,1,4) |
07 | 1(1,2,4) | 3(1,1,5)(2,2,3)(3,3,1) |
08 | 2(1,2,5)(1,3,4) | 3(1,1,6)(2,2,4)(3,3,2) |
09 | 3(1,2,6)(1,3,5)(2,3,4)(24) | 4(1,1,7)(2,2,5)(3,3,3)(4,4,1) |
10 | 4(1,2,7)(1,3,6)(1,4,5)(2,3,5) | 4(1,1,8)(2,2,6)(3,3,4)(4,4,2) |
11 | 5(1,2,8)(1,3,7)(1,4,6)(2,3,6)(2,4,5)(40) | 5(1,1,9)(2,2,7)(3,3,5)(4,4,3)(5,5,1) |
12 | 7(1,2,9)(1,3,8)(1,4,7)(1,5,6)(2,3,7)(2,4,6)(3,4,5)(60) | 5(1,1,10)(2,2,8)(3,3,6)(4,4,4)(5,5,2) |
13 | 8(1,2,10)(1,3,9)(1,4,8)(1,5,7)(2,3,8)(2,4,7)(2,5,6)(60)(3,4,6)(72) | 6(1,1,11)(2,2,9)(3,3,7)(4,4,5)(5,5,3)(6,6,1) |
14 | 10(1,2,11)(1,3,10)(1,4,9)(1,5,8)(1,6,7)(2,3,9)(2,4,8)(2,5,7)(3,4,7)(3,5,6)(90) | 6(1,1,12)(2,2,10)(3,3,8)(4,4,6)(5,5,4)(6,6,2) |
15 | 12 (1,2,12)(1,3,11)(1,4,10)(1,5,9)(1,6,8)(2,3,10)(2,4,9)(2,5,8)(2,6,7)(84)(3,4,8)(3,5,7)(105)(4,5,6)(120) | 7(1,1,13)(2,2,11)(3,3,9)(4,4,7)(5,5,5)(6,6,3)(7,7,1) |
16 | 14 ((1,2,13)(1,3,12)(1,4,11)(1,5,10)(1,6,9)(1,7,8)(2,3,11)(2,4,10)(2,5,9)(2,6,8)(3,4,9)(3,5,8)(3,6,7)(126)(4,5,7)(140) | 7(1,1,14)(2,2,12)(3,3,10)(4,4,8)(5,5,6)(6,6,4)(7,7,2) |
17 | 16(1,2,14)(1,3,13)(1,4,12)(1,5,11)(1,6,10)(1,7,9)(2,3,12)(2,4,11)(2,5,10)(2,6,9)(2,7,8)(112)(3,4,10)(3,5,9)(3,6,8)(144)(4,5,8)(160)(4,6,7)(168) | 8(1,1,15)(2,2,13)(3,3,11)(4,4,9)(5,5,7)(6,6,5)(7,7,3)(8,8,1) |
18 | 19(1,2,15)(1,3,14)(1,4,13)(1,5,12)(1,6,11)(1,7,10)(1,8,9)(2,3,13)(2,4,12)(2,5,11)(2,6,10)(2,7,9)(3,4,11)(3,5,10)(3,6,9)(3,7,8)(168)(4,5,9)(4,6,8)(192)(5,6,7)(210) | 8(1,1,16)(2,2,14)(3,3,12)(4,4,10)(5,5,8)(6,6,6)(7,7,4)(8,8,2) |
19 | 21(1,2,16)(1,3,15)(1,4,14)(1,5,13)(1,6,12)(1,7,11)(1,8,10)(2,3,14)(2,4,13)(2,5,12)(2,6,11)(2,7,10)(2,8,9)(144)(3,4,12)(3,5,11)(3,6,10)(3,7,9)(189)(4,5,10)(4,6,9)(216)(4,7,8)(224)(5,6,8)(240) | 9(1,1,17)(2,2,15)(3,3,13)(4,4,11)(5,5,9)(6,6,7)(7,7,5)(8,8,3)(9,9,1) |
20 | 24(1,2,17)(1,3,16)(1,4,15)(1,5,14)(1,6,13)(1,7,12)(1,8,11)(1,9,10)(2,3,15)(2,4,14)(2,5,13)(2,6,12)(2,7,11)(2,8,10)(3,4,13)(3,5,12)(3,6,11)(3,7,10)(3,8,9)(216)(4,5,11)(4,6,10)(4,7,9)(252)(5,6,9)(270)(5,7,8)(280) | 9(1,1,18)(2,2,16)(3,3,14)(4,4,12)(5,5,10)(6,6,8)(7,7,6)(8,8,4)(9,9,2) |
21 | 27(1,2,18)(1,3,17)(1,4,16)(1,5,15)(1,6,14)(1,7,13)(1,8,12)(1,9,11)(2,3,16)(2,4,15)(2,5,14)(2,6,13)(2,7,12)(2,8,11)(2,9,10)(180)(3,4,14)(3,5,13)(3,6,12)(3,7,11)(3,8,10)(240)(4,5,12)(4,6,11)(4,7,10)(280)(4,8,9)(288)(5,6,10)(300)(5,7,9)(315)(6,7,8)(336) | 10(1,1,19)(2,2,17)(3,3,15)(4,4,13)(5,5,11)(6,6,9)(7,7,7)(8,8,5)(9,9,3)(10,10,1) |
22 | 30(1,2,19)(1,3,18)(1,4,17)(1,5,16)(1,6,15)(1,7,14)(1,8,13)(1,9,12)(1,10,11)(2,3,17)(2,4,16)(2,5,15)(2,6,14)(2,7,13)(2,8,12)(2,9,11)(3,4,15)(3,5,14)(3,6,13)(3,7,12)(3,8,11)(3,9,10)(270)(4,5,13)(4,6,12)(4,7,11)(4,8,10)(320)(5,6,11)(5,7,10)(350)(5,8,9)(360)(6,7,9)(378) | 10(1,1,20)(2,2,18)(3,3,16)(4,4,14)(5,5,12)(6,6,10)(7,7,8)(8,8,6)(9,9,4)(10,10,2) |
23 | 33(1,2,20)(1,3,19)(1,4,18)(1,5,17)(1,6,16)(1,7,15)(1,8,14)(1,9,13)(1,10,12)(2,3,18)(2,4,17)(2,5,16)(2,6,15)(2,7,14)(2,8,13)(2,9,12)(2,10,11)(220)(3,4,16)(3,5,15)(3,6,14)(3,7,13)(3,8,12)(3,9,11)(297)(4,5,14)(4,6,13)(4,7,12)(4,8,11)(352)(4,9,10)(360)(5,6,12)(5,7,11)(385)(5,8,10)(400)(6,7,10)(420)(6,8,9)(432) | 11(1,1,21)(2,2,19)(3,3,17)(4,4,15)(5,5,13)(6,6,11)(7,7,9)(8,8,7)(9,9,5)(10,10,3)(11,11,1) |
24 | 37(1,2,21)(1,3,20)(1,4,19)(1,5,18)(1,6,17)(1,7,16)(1,8,15)(1,9,14)(1,10,13)(1,11,12)(2,3,19)(2,4,18)(2,5,17)(2,6,16)(2,7,15)(2,8,14)(2,9,13)(2,10,12)(3,4,17)(3,5,16)(3,6,15)(3,7,14)(3,8,13)(3,9,12)(3,10,11)(330)(4,5,15)(4,6,14)(4,7,13)(4,8,12)(4,9,11)(396)(5,6,13)(5,7,12)(5,8,11)(440)(5,9,10)(450)(6,7,11)(462)(6,8,10)(480)(7,8,9)(504) | 11(1,1,22)(2,2,20)(3,3,18)(4,4,16)(5,5,14)(6,6,12)(7,7,10)(8,8,8)(9,9,6)(10,10,4)(11,11,2) |
25 | 40(1,2,22)(1,3,21)(1,4,20)(1,5,19)(1,6,18)(1,7,17)(1,8,16)(1,9,15)(1,10,14)(1,11,13)(2,3,20)(2,4,19)(2,5,18)(2,6,17)(2,7,16)(2,8,15)(2,9,14)(2,10,13)(2,11,12)(264)(3,4,18)(3,5,17)(3,6,16)(3,7,15)(3,8,14)(3,9,13)(3,10,12)(360)(4,5,16)(4,6,15)(4,7,14)(4,8,13)(4,9,12)(432)(4,10,11)(440)(5,6,14)(5,7,13)(5,8,12)(480)(5,9,11)(495)(6,7,12)(504)(6,8,11)(528)(6,9,10)(540)(7,8,10)(560) | 12(1,1,23)(2,2,21)(3,3,19)(4,4,17)(5,5,15)(6,6,13)(7,7,11)(8,8,9)(9,9,7)(10,10,5)(11,11,3)(12,12,1) |
26 | 44(1,2,23)(1,3,22)(1,4,21)(1,5,20)(1,6,19)(1,7,18)(1,8,17)(1,9,16)(1,10,15)(1,11,14)(1,12,13)(2,3,21)(2,4,20)(2,5,19)(2,6,18)(2,7,17)(2,8,16)(2,9,15)(2,10,14)(2,11,13)(3,4,19)(3,5,18)(3,6,17)(3,7,16)(3,8,15)(3,9,14)(3,10,13)(3,11,12)(396)(4,5,17)(4,6,16)(4,7,15)(4,8,14)(4,9,13)(4,10,12)(480)(5,6,15)(5,7,14)(5,8,13)(5,9,12)(540)(5,10,11)(550)(6,7,13)(6,8,12)(576)(6,9,11)(594)(7,8,11)(616)(7,9,10)(630) | 12(1,1,24)(2,2,22)(3,3,20)(4,4,18)(5,5,16)(6,6,14)(7,7,12)(8,8,10)(9,9,8)(10,10,6)(11,11,4)(12,12,2) |
27 | 48(1,2,24)(1,3,23)(1,4,22)(1,5,21)(1,6,20)(1,7,19)(1,8,18)(1,9,17)(1,10,16)(1,11,15)(1,12,14)(2,3,22)(2,4,21)(2,5,20)(2,6,19)(2,7,18)(2,8,17)(2,9,16)(2,10,15)(2,11,14)(2,12,13)(312)(3,4,20)(3,5,19)(3,6,18)(3,7,17)(3,8,16)(3,9,15)(3,10,14)(3,11,13)(429)(4,5,18)(4,6,17)(4,7,16)(4,8,15)(4,9,14)(4,10,13)(520)(4,11,12)(528)(5,6,16)(5,7,15)(5,8,14)(5,9,13)(585)(5,10,12)(600)(6,7,14)(6,8,13)(624)(6,9,12)(648)(6,10,11)(660)(7,8,12)(672)(7,9,11)(693)(8,9,10)(720) | 13(1,1,25)(2,2,23)(3,3,21)(4,4,19)(5,5,17)(6,6,15)(7,7,13)(8,8,11)(9,9,9)(10,10,7)(11,11,5)(12,12,3)(13,13,1) |
28 | 52(1,2,25)(1,3,24)(1,4,23)(1,5,22)(1,6,21)(1,7,20)(1,8,19)(1,9,18)(1,10,17)(1,11,16)(1,12,15)(1,13,14)(2,3,23)(2,4,22)(2,5,21)(2,6,20)(2,7,19)(2,8,18)(2,9,17)(2,10,16)(2,11,15)(2,12,14)(3,4,21)(3,5,20)(3,6,19)(3,7,18)(3,8,17)(3,9,16)(3,10,15)(3,11,14)(3,12,13)(468)(4,5,19)(4,6,18)(4,7,17)(4,8,16)(4,9,15)(4,10,14)(4,11,13)(572)(5,6,17)(5,7,16)(5,8,15)(5,9,14)(5,10,13)(650)(5,11,12)(660)(6,7,15)(6,8,14)(6,9,13)(702)(6,10,12)(720)(7,8,13)(728)(7,9,12)(756)(7,10,11)(770)(8,9,11)(792) | 13(1,1,26)(2,2,24)(3,3,22)(4,4,20)(5,5,18)(6,6,16)(7,7,14)(8,8,12)(9,9,10)(10,10,8)(11,11,6)(12,12,4)(13,13,2) |
29 | 56(1,2,26)(1,3,25)(1,4,24)(1,5,23)(1,6,22)(1,7,21)(1,8,20)(1,9,19)(1,10,18)(1,11,17)(1,12,16)(1,13,15)(2,3,24)(2,4,23)(2,5,22)(2,6,21)(2,7,20)(2,8,19)(2,9,18)(2,10,17)(2,11,16)(2,12,15)(2,13,14)(364)(3,4,22)(3,5,21)(3,6,20)(3,7,19)(3,8,18)(3,9,17)(3,10,16)(3,11,15)(3,12,14)(504)(4,5,20)(4,6,19)(4,7,18)(4,8,17)(4,9,16)(4,10,15)(4,11,14)(616)(4,12,13)(624)(5,6,18)(5,7,17)(5,8,16)(5,9,15)(5,10,14)(700)(5,11,13)(715)(6,7,16)(6,8,15)(6,9,14)(756)(6,10,13)(780)(6,11,12)(792)(7,8,14)(784)(7,9,13)(819)(7,10,12)(840)(8,9,12)(864)(8,10,11)(880) | 14(1,1,27)(2,2,25)(3,3,23)(4,4,21)(5,5,19)(6,6,17)(7,7,15)(8,8,13)(9,9,11)(10,10,9)(11,11,7)(12,12,5)(13,13,3)(14,14,1) |
30 | 61(1,2,27)(1,3,16)(1,4,25)(1,5,24)(1,6,23)(1,7,22)(1,8,21)(1,9,20)(1,10,19)(1,11,18)(1,12,17)(1,13,16)(1,14,15)(2,3,25)(2,4,24)(2,5,23)(2,6,22)(2,7,21)(2,8,20)(2,9.19)(2,10,18)(2,11,17)(2,12,16)(2,13,15)(3,4,23)(3,5,22)(3,6,21)(3,7,20)(3,8,19)(3,9,18)(3,10,17)(3,11,16)(3,12,15)(3,13,14)(4,5,21)(4,6,20)(4,7,19)(4,8,18)(4,9,17)(4,10,16)(4,11,15)(4,12,14)(5,6,19)(5,7,18)(5,8,17)(5,9,16)(5,10,15)(5,11,14)(5,12,13)(6,7,17)(6,8,16)(6,9,15)(6,10,14)(6,11,13)(7,8,15)(7,9,14)(7,10,13)(7,11,12)(8,9,13)(8,10,12)(9,10,11) | 14(1,1,28)(2,2,26)(3,3,24)(4,4,22)(5,5,20)(6,6,18)(7,7,16)(8,8,14)(9,9,12)(10,10,10)(11,11,8)(12,12,6)(13,13,4)(14,14,2) |
31 | 65(1,2,28)(1,3,27)(1,4,26)(1,5,25)(1,6,24)(1,7,23)(1,8,22)(1,9,21)(1,10,20)(1,11,19)(1,12,18)(1,13,17)(1,14,16)(2,3,26)(2,4,25)(2,5,24)(2,6,23)(2,7,22)(2,8,21)(2,9,20)(2,10,19)(2,11,18)(2,12,17)(2,13,16)(2,14,15)(3,4,24)(3,5,23)(3,6,22)(3,7,21)(3,8,20)(3,9,19)(3,10,18)(3,11,17)(3,12,16)(3,13,15)(4,5,22)(4,6,21)(4,7,20)(4,8,19)(4,9,18)(4,10,17)(4,11,16)(4,12,15)(4,13,14)(5,6,20)(5,7,19)(5,8,18)(5,9,17)(5,10,16)(5,11,15)(5,12,14)(6,7,18)(6,8,17)(6,9,16)(6,10,15)(6,11,14)(6,12,13)(7,8,16)(7,9,15)(7,10,14)(7,11,13)(8,9,14)(8,10,13)(8,11,12)(9,10,12) | 15(1,1,29)(2,2,27)(3,3,25)(4,4,23)(5,5,21)(6,6,19)(7,7,17)(8,8,15)(9,9,13)(10,10,11)(11,11,9)(12,12,7)(13,13,5)(14,14,3)(15,15,1) |
32 | 70(1,2,29)(1,3,28)(1,4,27)(1,5,26)(1,6,25)(1,7,24)(1,8,23)(1,9,22)(1,10,21)(1,11,20)(1,12,19)(1,13,18)(1,14,17)(1,15,16)(2,3,27)(2,4,26)(2,5,25)(2,6,24)(2,7,23)(2,8,22)(2,9,21)(2,10,20)(2,11,19)(2,12,18)(2,13,17)(2,14,16)(3,4,25)(3,5,24)(3,6,23)(3,7,22)(3,8,21)(3,9,20)(3,10,19)(3,11,18)(3,12,17)(3,13,16)(3,14,15)(4,5,23)(4,6,22)(4,7,21)(4,8,20)(4,9,19)(4,10,18)(4,11,17)(4,12,16)(4,13,15)(5,6,21)(5,7,20)(5,8,19)(5,9,18)(5,10,17)(5,11,16)(5,12,15)(5,13,14)(6,7,19)(6,8,18)(6,9,17)(6,10,16)(6,11,15)(6,12,14)(7,8,17)(7,9,16)(7,10,15)(7,11,14)(7,12,13)(8,9,15)(8,10,14)(8,11,13)(9,10,13)(9,11,12) | 15(1,1,30)(2,2,28)(3,3,26)(4,4,24)(5,5,22)(6,6,20)(7,7,18)(8,8,16)(9,9,14)(10,10,12)(11,11,10)(12,12,8)(13,13,6)(14,14,4)(15,15,2) |
33 | 75(1,2,30)(1,3,29)(1,4,28)(1,5,27)(1,6,26)(1,7,25)(1,8,24)(1,9,23)(1,10,22)(1,11,21)(1,12,20)(1,13,19)(1,14,18)(1,15,17)(2,3,28)(2,4,27)(2,5,26)(2,6,25)(2,7,24)(2,8,23)(2,9,22)(2,10,21)(2,11,20)(2,12,19)(2,13,18)(2,14,17)(2,15,16)(3,4,26)(3,5,25)(3,6,24)(3,7,23)(3,8,22)(3,9,21)(3,10,20)(3,11,19)(3,12,18)(3,13,17)(3,14,16)(4,5,24)(4,6,23)(4,7,22)(4,8,21)(4,9,20)(4,10,19)(4,11,18)(4,12,17)(4,13,16)(4,14,15)(5,6,22)(5,7,21)(5,8,20)(5,9,19)(5,10,18)(5,11,17)(5,12,16)(5,13,15)(6,7,20)(6,8,19)(6,9,18)(6,10,17)(6,11,16)(6,12,15)(6,13,14)(7,8,18)(7,9,17)(7,10,16)(7,11,15)(7,12,14)(8,9,16)(8,10,15)(8,11,14)(8,12,13)(9,10,14)(9,11,13)(10,11,12) | 16(1,1,31)(2,2,29)(3,3,27)(4,4,25)(5,5,23)(6,6,21)(7,7,19)(8,8,17)(9,9,15)(10,10,13)(11,11,11)(12,12,9)(13,13,7)(14,14,5)(15,15,3)(16,16,1) |
34 | 80(1,2,31)(1,3,30)(1,4,29)(1,5,28)(1,6,27)(1,7,26)(1,8,25)(1,9,24)(1,10,23)(1,11,22)(1,12,21)(1,13,20)(1,14,19)(1,15,18)(1,16,17)(2,3,29)(2,4,28)(2,5,27)(2,6,26)(2,7,25)(2,8,24)(2,9,23)(2,10,22)(2,11,21)(2,12,20)(2,13,19)(2,14,18)(2,15,17)(3,4,27)(3,5,26)(3,6,25)(3,7,24)(3,8,23)(3,9,22)(3,10,21)(3,11,20)(3,12,19)(3,13,18)(3,14,17)(3,15,16)(4,5,25)(4,6,24)(4,7,23)(4,8,22)(4,9,21)(4,10,20)(4,11,19)(4,12,18)(4,13,17)(4,14,16)(5,6,23)(5,7,22)(5,8,21)(5,9,20)(5,10,19)(5,11,18)(5,12,17)(5,13,16)(5,14,15)(6,7,21)(6,8,20)(6,9,19)(6,10,18)(6,11,17)(6,12,16)(6,13,15)(7,8,19)(7,9,18)(7,10,17)(7,11,16)(7,12,15)(7,13,14)(8,9,17)(8,10,16)(8,11,15)(8,12,14)(9,10,15)(9,11,14)(9,12,13)(10,11,13) | 16(1,1,32)(2,2,30)(3,3,28)(4,4,26)(5,5,24)(6,6,22)(7,7,20)(8,8,18)(9,9,16)(10,10,14)(11,11,12)(12,12,10)(13,13,8)(14,14,6)(15,15,4)(16,16,2) |
35 | 85(1,2,32)(1,3,31)(1,4,30)(1,5,29)(1,6,28)(1,7,27)(1,8,26)(1,9,25)(1,10,24)(1,11,23)(1,12,22)(1,13,21)(1,14,20)(1,15,19)(1,16,18)(2,3,30)(2,4,29)(2,5,28)(2,6,27)(2,7,26)(2,8,25)(2,9,24)(2,10,23)(2,11,22)(2,12,21)(2,13,20)(2,14,19)(2,15,18)(2,16,17)(3,4,28)(3,5,27)(3,6,26)(3,7,25)(3,8,24)(3,9,23)(3,10,22)(3,11,21)(3,12,20)(3,13,19)(3,14,18)(3,15,17)(4,5,26)(4,6,25)(4,7,24)(4,8,23)(4,9,22)(4,10,21)(4,11,20)(4,12,19)(4,13,18)(4,14,17)(4,15,16)(5,6,24)(5,7,23)(5,8,22)(5,9,21)(5,10,20)(5,11,19)(5,12,18)(5,13,17)(5,14,16)(6,7,22)(6,8,21)(6,9,20)(6,10,19)(6,11,18)(6,12,17)(6,13,16)(6,14,15)(7,8,20)(7,9,19)(7,10,18)(7,11,17)(7,12,16)(7,13,15)(8,9,18)(8,10,17)(8,11,16)(8,12,15)(8,13,14)(9,10,16)(9,11,15)(9,12,14)(10,11,14)(10,12,13) | |
36 | 91(1,2,33)(1,3,32)(1,4,31)(1,5,30)(1,6,29)(1,7,28)(1,8,27)(1,9,26)(1,10,25)(1,11,24)(1,12,23)(1,13,22)(1,14,21)(1,15,20)(1,16,19)(1,17,18)(2,3,31)(2,4,30)(2,5,29)(2,6,28)(2,7,27)(2,8,26)(2,9,25)(2,10,24)(2,11,23)(2,12,22)(2,13,21)(2,14,20)(2,15,19)(2,16,18)(3,4,29)(3,5,28)(3,6,27)(3,7,26)(3,8,25)(3,9,24)(3,10,23)(3,11,22)(3,12,21)(3,13,20)(3,14,19)(3,15,18)(3,16,17)(4,5,27)(4,6,26)(4,7,25)(4,8,24)(4,9,23)(4,10,22)(4,11,21)(4,12,20)(4,13,19)(4,14,18)(4,15,17)(5,6,25)(5,7,24)(5,8,23)(5,9,22)(5,10,21)(5,11,20)(5,12,19)(5,13,18)(5,14,17)(5,15,16)(6,7,23)(6,8,22)(6,9,21)(6,10,20)(6,11,19)(6,12,18)(6,13,17)(6,14,16)(7,8,21)(7,9,20)(7,10,19)(7,11,18)(7,12,17)(7,13,16)(7,14,15)(8,9,19)(8,10,18)(8,11,17)(8,12,16)(8,13,15)(9,10,17)(9,11,16)(9,12,15)(9,13,14)(10,11,15)(10,12,14)(11,12,13) | |
37 | 96(1,2,34)(1,3,33)(1,4,32)(1,5,31)(1,6,30)(1,7,29)(1,8,28)(1,9,27)(1,10,26)(1,11,25)(1,12,24)(1,13,23)(1,14,22)(1,15,21)(1,16,20)(1,17,19)(2,3,32)(2,4,31)(2,5,30)(2,6,29)(2,7,28)(2,8,27)(2,9,26)(2,10,25)(2,11,24)(2,12,23)(2,13,22)(2,14,21)(2,15,20)(2,16,19)(2,17,18)(3,4,30)(3,5,29)(3,6,28)(3,7,27)(3,8,26)(3,9,25)(3,10,24)(3,11,23)(3,12,22)(3,13,21)(3,14,20)(3,15,19)(3,16,18)(4,5,28)(4,6,27)(4,7,26)(4,8,25)(4,9,24)(4,10,23)(4,11,22)(4,12,21)(4,13,20)(4,14,19)(4,15,18)(4,16,17)(5,6,26)(5,7,25)(5,8,24)(5,9,23)(5,10,22)(5,11,21)(5,12,20)(5,13,19)(5,14,18)(5,15,17)(6,7,24)(6,8,23)(6,9,22)(6,10,21)(6,11,20)(6,12,19)(6,13,18)(6,14,17)(6,15,16)(7,8,22)(7,9,21)(7,10,20)(7,11,19)(7,12,18)(7,13,17)(7,14,16)(8,9,20)(8,10,19)(8,11,18)(8,12,17)(8,13,16)(8,14,15)(9,10,18)(9,11,17)(9,12,16)(9,13,15)(10,11,16)(10,12,15)(10,13,14)(11,12,14) | |
38 | 102(1,2,35)(1,3,34)(1,4,33)(1,5,32)(1,6,31)(1,7,30)(1,8,29)(1,9,28)(1,10,27)(1,11,26)(1,12,25)(1,13,24)(1,14,23)(1,15,22)(1,16,21)(1,17,20)(1,18,19)(2,3,33)(2,4,32)(2,5,31)(2,6,30)(2,7,29)(2,8,28)(2,9,27)(2,10,26)(2,11,25)(2,12,24)(2,13,23)(2,14,22)(2,15,21)(2,16,20)(2,17,19)(3,4,31)(3,5,30)(3,6,29)(3,7,28)(3,8,27)(3,9,26)(3,10,25)(3,11,24)(3,12,23)(3,13,22)(3,14,21)(3,15,20)(3,16,19)(3,17,18)(4,5,29)(4,6,28)(4,7,27)(4,8,26)(4,9,25)(4,10,24)(4,11,23)(4,12,22)(4,13,21)(4,14,20)(4,15,19)(4,16,18)(5,6,27)(5,7,26)(5,8,25)(5,9,24)(5,10,23)(5,11,22)(5,12,21)(5,13,20)(5,14,19)(5,15,18)(5,16,17)(6,7,25)(6,8,24)(6,9,23)(6,10,22)(6,11,21)(6,12,20)(6,13,19)(6,14,18)(6,15,17)(7,8,23)(7,9,22)(7,10,21)(7,11,20)(7,12,19)(7,13,18)(7,14,17)(7,15,16)(8,9,21)(8,10,20)(8,11,19)(8,12,18)(8,13,17)(8,14,16)(9,10,19)(9,11,18)(9,12,17)(9,13,16)(9,14,15)(10,11,17)(10,12,16)(10,13,15)(11,12,15)(11,13,14) | |
39 | 107(1,2,36)(1,3,35)(1,4,34)(1,5,33)(1,6,32)(1,7,31)(1,8,30)(1,9,29)(1,10,28)(1,11,27)(1,12,26)(1,13,25)(1,14,24)(1,15,23)(1,16,22)(1,17,21)(1,18,20)(2,3,34)(2,4,33)(2,5,32)(2,6,31)(2,7,30)(2,8,29)(2,9,28)(2,10,27)(2,11,26)(2,12,25)(2,13,24)(2,14,23)(2,15,22)(2,16,21)(2,17,20)(2,18,19)(3,4,32)(3,5,31)(3,6,30)(3,7,29)(3,8,28)(3,9,27)(3,10,26)(3,11,25)(3,12,24)(3,13,23)(3,14,22)(3,15,21)(3,16,20)(3,17,19)(4,5,30)(4,6,29)(4,7,28)(4,8,27)(4,9,26)(4,10,25)(4,11,24)(4,12,23)(4,13,22)(4,14,21)(4,15,20)(4,16,19)(4,17,18)(5,6,28)(5,7,27)(5,8,26)(5,9,25)(5,10,24)(5,11,23)(5,12,22)(5,13,21)(5,14,20)(5,15,19)(5,16,18)(6,7,26)(6,8,25)(6,9,24)(6,10,23)(6,11,22)(6,12,21)(6,13,20)(6,14,19)(6,15,18)(6,16,17)(7,8,24)(7,9,23)(7,10,22)(7,11,21)(7,12,20)(7,13,19)(7,14,18)(7,15,17)(8,9,22)(8,10,21)(8,11,20)(8,12,19)(8,13,18)(8,14,17)(8,15,16)(9,10,20)(9,11,19)(9,12,18)(9,13,17)(9,14,16)(10,11,18)(10,12,17)(10,13,16)(10,14,15)(11,12,16)(11,13,15)(12,13,14) | |
40 | 114(1,2,37)(1,3,36)(1,4,35)(1,5,34)(1,6,33)(1,7,32)(1,8,31)(1,9,30)(1,10,29)(1,11,28)(1,12,27)(1,13,26)(1,14,25)(1,15,24)(1,16,23)(1,17,22)(1,18,21)(1,19,20)(2,3,35)(2,4,34)(2,5,33)(2,6,32)(2,7,31)(2,8,30)(2,9,29)(2,10,28)(2,11,27)(2,12,26)(2,13,25)(2,14,24)(2,15,23)(2,16,22)(2,17,21)(2,18,20)(3,4,33)(3,5,32)(3,6,31)(3,7,30)(3,8,29)(3,9,28)(3,10,27)(3,11,26)(3,12,25)(3,13,24)(3,14,23)(3,15,22)(3,16,21)(3,17,20)(3,18,19)(4,5,31)(4,6,30)(4,7,29)(4,8,28)(4,9,27)(4,10,26)(4,11,25)(4,12,24)(4,13,23)(4,14,22)(4,15,21)(4,16,20)(4,17,19)(5,6,29)(5,7,28)(5,8,27)(5,9,26)(5,10,25)(5,11,24)(5,12,23)(5,13,22)(5,14,21)(5,15,20)(5,16,19)(5,17,18)(6,7,27)(6,8,26)(6,9,25)(6,10,24)(6,11,23)(6,12,22)(6,13,21)(6,14,20)(6,15,19)(6,16,18)(7,8,25)(7,9,24)(7,10,23)(7,11,22)(7,12,21)(7,13,20)(7,14,19)(7,15,18)(7,16,17)(8,9,23)(8,10,22)(8,11,21)(8,12,20)(8,13,19)(8,14,18)(8,15,17)(9,10,21)(9,11,20)(9,12,19)(9,13,18)(9,14,17)(9,15,16)(10,11,19)(10,12,18)(10,13,17)(10,14,16)(11,12,17)(11,13,16)(11,14,15)(12,13,15) | |
41 | 120(1,2,38)(1,3,37)(1,4,36)(1,5,35)(1,6,34)(1,7,33)(1,8,32)(1,9,31)(1,10,30)(1,11,29)(1,12,28)(1,13,27)(1,14,26)(1,15,25)(1,16,24)(1,17,23)(1,18,22)(1,19,21)(2,3,36)(2,4,35)(2,5,34)(2,6,33)(2,7,32)(2,8,31)(2,9,30)(2,10,29)(2,11,28)(2,12,27)(2,13,26)(2,14,25)(2,15,24)(2,16,23)(2,17,22)(2,18,21)(2,19,20)(760)(3,4,34)(3,5,33)(3,6,32)(3,7,31)(3,8,30)(3,9,29)(3,10,28)(3,11,27)(3,12,26)(3,13,25)(3,14,24)(3,15,23)(3,16,22)(3,17,21)(3,18,20)(1080)(4,5,32)(4,6,31)(4,7,30)(4,8,29)(4,9,28)(4,10,27)(4,11,26)(4,12,25)(4,13,24)(4,14,23)(4,15,22)(4,16,21)(4,17,20)(1360)(4,18,19)(1368)(5,6,30)(5,7,29)(5,8,28)(5,9,27)(5,10,26)(5,11,25)(5,12,24)(5,13,23)(5,14,22)(5,15,21)(5,16,20)(1600)(5,17,19)(1615)(6,7,28)(6,8,27)(6,9,26)(6,10,25)(6,11,24)(6,12,23)(6,13,22)(6,14,21)(6,15,20)(1800)(6,16,19)(1824)(6,17,18)(1836)(7,8,26)(7,9,25)(7,10,24)(7,11,23)(7,12,22)(7,13,21)(7,14,20)(1960)(7,15,19)(1995)(7,16,18)(2016)(8,9,24)(8,10,23)(8,11,22)(8,12,21)(8,13,20)(2080)(8,14,19)(2128)(8,15,18)(2160)(8,16,17)(2176)(9,10,22)(9,11,21)(9,12,20)(2160)(9,13,19)(2223)(9,14,18)(2268)(9,15,17)(2295)(10,11,20)(2200)(10,12,19)(2280)(10,13,18)(2340)(10,14,17)(2380)(10,15,16)(2400)(11,12,18)(2376)(11,13,17)(2431)(11,14,16)(2464)(12,13,16)(2496)(12,14,15)(2520) | |
* Blue colored triplets indicate where triangles can be formed & red colored triplets indicate triangles are right angled.
* Green colored figures indicate product of the triplets where triangles are formed.
* For no. of combinations, triplets are represented as (a,b,c). For every (a,b,c) which forms a triangle (given by blue/red color) in without repetition arrangement, there exists an (a',b',c') within the same no. such that (a'.b',c') may or may not form triangles. And For every (a,b,c) which forms a triangle (given by blue color) with repetition arrangement, there exists an (a',b',c') within the same no. such that (a'.b',c') also forms triangles in some cases and do not form triangles in some cases. a'=b+c-a, b'=a+c-b, c'=a+b-c. We call (a'.b',c') child triplet. Exa:- For 18,if triangle triplet is (4,6,8), child triplet is (10,6,2) which lies within 18 but does not form triangle. For arrangement with repetition, if triangle triplet is (5,5,8), child triplet is (8,8,2) which lies in triangle triplets whereas if triangle triplet is (7,7,4), child triplet (4,4,10) lies out of the triangle triplets. Just put the value of (a,b,c) for triangle triplets(either from with or without repetition arrangement) and submit and the child (a',b',c') will appear. For instance in case of no. 18, put (3,7,8) and child (2,4,12) will appear.
* In the table, bracket figures are (non-child + child). - means child triplet does not exist.
* If the triplets are not pythagorean triplets, (len1*a'b'c') will not be a perfect square.
(*) To find total arrangement , visit http://www.mathaddict.net/comm4b.htm . This is an arrangement with ordering. For example, if sum of 3 numbers is 6, arrangements without ordering are (1,2,3),(2,2,2)(1,1,4). But on ordering, (1,2,3) becomes (1,2,3)(1,3,2),(2,1,3),(3,1,2),(2,3,1),(3,2,1) i.e 3! for all 3 elements being dissimilar. (2,2,2) remains same as all elements are similar. (1,1,4) becomes (1,1,4),(1,4,1),(4,1,1) i.e C(3,2)=3. Thus total arrangement becomes 10 from 3.
SUM of 3 numbers | Arrangement-without repetition (non-child +child) |
Arrangement where triangle formed | Arrangement-with repetition (non- child + child) |
Arrangement where
triangle formed
|
Total arrangement (non-child+child) |
Total arrangement
where triangle formed
|
Total arrangement with ordering (*) |
3 | 0 | 0 | 1 (-+0) | 1 | 1(0+0) | 1 | 1 |
4 | 0 | 0 | 1 (1+-) | 0 | 1(1+0) | 0 | 3 |
5 | 0 | 0 | 2 (0+1) | 1 | 2(0+1) | 1 | 6 |
6 | 1 (1+-) | 0 | 2 (1+0) | 1 | 3(2+0) | 1 | 10 |
7 | 1 (1+-) | 0 | 3 (0+1) | 2 | 4(1+1) | 2 | 15 |
8 | 2 (2+-) | 0 | 3 (1+1) | 1 | 5(3+1) | 1 | 21 |
9 | 3 (1+1) | 1 | 4 (1+1) | 2 | 7(2+2) | 3 | 28 |
10 | 4 (4+-) | 0 | 4 (1+1) | 2 | 8(5+1) | 2 | 36 |
11 | 5 (3+1) | 1 | 5 (1+1) | 3 | 10(4+2) | 4 | 45 |
12 | 7 (5+1) | 1 | 5 (2+1) | 2 | 12(7+2) | 3 | 55 |
13 | 8 (4+2) | 2 | 6 (1+2) | 3 | 14(5+4) | 5 | 66 |
14 | 10 (8+1) | 1 | 6 (2+1) | 3 | 16(10+2) | 4 | 78 |
15 | 12 (7+2) | 3 | 7 (1+2) | 4 | 19(8+4) | 7 | 91 |
16 | 14 (10+2) | 2 | 7 (2+2) | 3 | 21(12+4) | 5 | |
17 | 16 (8+4) | 4 | 8 (2+2) | 4 | 24(10+6) | 8 | |
18 | 19 (14+2) | 3 | 8 (2+2) | 4 | 27(16+4) | 7 | |
19 | 21 (12+4) | 5 | 9 (2+2) | 5 | 30(14+6) | 10 | |
20 | 24 (16+4) | 4 | 9 (3+2) | 4 | 33(19+6) | 8 | |
21 | 27 (14+6) | 7 | 10(2+3) | 5 | 37(16+9) | 12 | |
22 | 30 (21+4) | 5 | 10(3+2) | 5 | 40(24+6) | 10 | |
23 | 33 (19+6) | 8 | 11(2+3) | 6 | 44(21+9) | 14 | |
24 | 37 (24+6) | 7 | 11(3+3) | 5 | 48(27+9) | 12 | |
25 | 40 (21+9) | 10 | 12(3+3) | 6 | 52(24+12) | 16 | |
26 | 44 (30+6) | 8 | 12(3+3) | 6 | 56(33+9) | 14 | |
27 | 48 (27+9) | 12 | 13(3+3) | 7 | 61(30+12) | 19 | |
28 | 52 (33+9) | 10 | 13(4+3) | 6 | 65(37+12) | 16 | |
29 | 56 (30+12) | 14 | 14(3+4) | 7 | 70(33+16) | 21 | |
30 | 61 (40+9) | 12 | 14(4+3) | 7 | 75(44+12) | 19 | |
31 | 65 (37+12) | 16 | 15(3+4) | 8 | 80(40+16) | 24 | |
32 | 70 (44+12) | 14 | 15(4+4) | 7 | 85(48+16) | 21 | |
33 | 75 (40+16) | 19 | 16(4+4) | 8 | 91(44+20) | 27 | |
34 | 80 (52+12) | 16 | 16(4+4) | 8 | 96(56+16) | 24 | |
35 | 85 (48+16) | 21 | 17(4+4) | 9 | |||
36 | 91 (56+16) | 19 | 17(5+4) | 8 | |||
37 | 96 (52+20) | 24 | 18(4+5) | 9 | |||
38 | 102(65+16) | 21 | 18(5+4) | 9 | |||
39 | 108(61+20) | 27 | 19(4+5) | 10 | |||
40 | 114(70+20) | 24 | 19(5+5) | 9 | |||
41 | 120(65+25) | 30 | 20(5+5) | 10 | |||