Soluţii corecte: Zoltan Szabo,  Ionel-Vasile Pit-Rada (fara pozitionarea pionului in casuta initial libera), Vasile Trofin, Nicu Scutaru.

Problema a fost propusa de Stefan Gatachiu, care a primit punctajul aferent acesteia (10 puncte). Multumim pentru propunere!

 

Zoltan Szabo:

Toate soluțiile de mai jos au proprietatea, că după ultimul pas, singura piesă rămasă pe tablă va ajunge în poziția unde era piesa lipsă pe tabla inițială. adică se obține negativul configurației inițiale.

6

(18,6) (30,18) (22,24) (18,30) (36,24) (20,22) (33,21) (22,20) (19,21) (31,19) (32,20) (34,22) (35,23) (16,28) (24,22) (28,16) (15,27) (19,21) (27,15) (9,21) (13,15) (21,9) (1,13) (2,14) (13,15) (4,2) (15,3) (2,4) (5,3) (16,4) (3,5) (6,4) (17,5) (4,6)

5

(17,5) (15,17) (18,16) (30,18) (22,24) (18,30) (20,22) (33,21) (22,20) (19,21) (31,19) (32,20) (34,22) (35,23) (36,24) (13,25) (21,19) (25,13) (13,15) (16,28) (24,22) (28,16) (6,18) (15,17) (18,16) (1,13) (2,14) (13,15) (4,2) (15,3) (2,4) (5,3) (16,4) (3,5)

4

(6,4) (18,6) (10,12) (6,18) (24,12) (16,18) (12,24) (30,18) (22,24) (18,30) (36,24) (35,23) (24,22) (21,23) (34,22) (23,21) (20,22) (33,21) (22,20) (31,33) (25,27) (33,21) (15,27) (19,21) (27,15) (9,21) (13,15) (21,9) (1,13) (2,14) (13,15) (4,2) (15,3) (2,4)

10

(22,10) (4,16) (6,4) (12,10) (10,22) (18,16) (22,10) (24,22) (21,23) (36,24) (24,22) (35,23) (23,21) (34,22) (4,16) (32,34) (21,33) (34,32) (31,33) (25,27) (33,21) (13,25) (21,19) (25,13) (7,19) (15,13) (19,7) (1,13) (2,14) (13,15) (16,14) (3,15) (14,16) (22,10)

11

(23,11) (15,17) (18,16) (21,23) (24,22) (36,24) (35,23) (23,21) (34,22) (21,23) (24,22) (33,21) (31,33) (25,27) (27,15) (19,21) (15,27) (33,21) (13,15) (1,13) (16,14) (6,18) (5,17) (18,16) (13,15) (2,14) (21,23) (10,22) (14,16) (3,15) (22,10) (4,16) (15,17) (23,11)

16

(4,16) (6,4) (12,10) (24,12) (16,18) (12,24) (30,18) (22,24) (18,30) (36,24) (35,23) (24,22) (21,23) (34,22) (23,21) (20,22) (33,21) (22,20) (31,33) (25,27) (33,21) (13,25) (21,19) (25,13) (7,19) (15,13) (19,7) (1,13) (2,14) (13,15) (4,16) (16,14) (3,15) (14,16)

 

Ionel-Vasile Pit-Rada (fara pozitionarea pionului in casuta initial libera):

Cele 6 solutii ar putea fi urmatoarele

Pion lipsa 4: (6,4) (18,6) (3,5) (10,12) (1,3) (22,10) (14,16) (23,11) (20,22) (35,23) (6,4) (33,35) (4,2) (36,34) (24,36) (16,4) (27,29) (13,1) (25,13) (1,3) (31,33) (12,10) (33,35) (36,34) (4,2) (2,14) (13,15) (29,17) (9,11) (11,23) (23,21) (15,27) (26,28) (34,22) 

Pion lipsa 5: (3,5) (15,3) (2,4) (13,15) (21,9) (33,21) (35,33) (22,34) (20,22) (30,28) (5,3) (25,27) (3,15) (17,5) (15,17) (17,29) (33,21) (28,16) (1,13) (19,7) (31,33) (7,9) (16,4) (18,30) (33,35) (6,18) (36,24) (18,30) (5,3) (3,15) (15,27) (30,28) (27,29) (35,23)

Pion lipsa 6: (4,6) (16,4) (3,5) (15,3) (13,15) (21,9) (28,16) (1,13) (26,14) (12,10) (6,4) (9,11) (3,1) (30,28) (13,15) (27,29) (25,13) (16,14) (13,15) (24,22) (35,23) (18,16) (16,14) (33,35) (31,33) (14,2) (36,34) (1,3) (3,5) (33,35) (5,17) (17,29) (35,23) (23,21) 

Pion lipsa 10: (12,10) (24,12) (9,11) (36,24) (16,18) (7,9) (12,10) (18,30) (34,36) (22,24) (4,16) (19,7) (32,34) (2,4) (1,13) (21,19) (15,17) (5,3) (19,7) (34,22) (31,19) (30,18) (26,28) (28,30) (36,24) (24,12) (6,18) (18,16) (22,10) (10,8) (7,9) (3,15) (15,13) (13,25)

Pion lipsa 11: (23,11) (35,23) (27,29) (23,35) (5,17) (25,27) (3,5) (1,3) (14,2) (6,4) (13,1) (18,6) (16,18) (21,23) (24,22) (3,5) (9,11) (19,21) (1,3) (6,4) (21,23) (33,21) (15,27) (36,24) (34,36) (18,30) (36,24) (31,33) (3,5) (24,22) (5,17) (33,21) (21,23) (23,11) 

Pion lipsa 16: (4,16) (12,10) (23,11) (16,4) (5,17) (35,23) (18,16) (8,10) (15,17) (33,35) (20,8) (27,29) (3,5) (23,11) (1,3) (25,27) (30,18) (13,1) (36,34) (21,23) (11,9) (6,4) (4,2) (29,17) (31,33) (34,32) (1,3) (3,15) (18,16) (16,14) (8,20) (19,21) (21,33) (32,34) 

 

Vasile Trofin:

Faptul ca la sfârsitul jocului ramane un pion în caseta care la începutul jocului era libera , se deduce ca jocul are un numar minim de mutari, respectiv 34. 

1) Pentru careurile cu caseta libera ( neocupata initial) 5 si 10 , jocul se poate termina în  34 de mutari ale pionului conform regulei stabilita de autor , respectiv numarul minim:

a) pentru caseta libera cu numarul 5 , mutarile sunt :

(3,5), (1,3), (14,2), (10,8), (22,10), (18,16), (6,18), (5,17), (24,12), (21,9), (36,24), (3,15), (23,11), (35,23), (7,9), (10,8), (2,14), (33,21), (24,22), (25,27), (31,33), (12,10), (21,9), (13,15), (19,21), (33,35), (27,29), (35,23), (15,17), (17,29), (21,23), (29,17), (9,11), (17,5).

b) pentru caseta libera cu numarul 10 , mutarile sunt :

(22,10), (24,22), (36,24), (18,16), (5,17), (16,28),  (3,5) , (1,3), (30,18), (18,24), (6,4), (24,22), (33,35), (35,23), ( 3,5), (13,1), (14,2), (26,14), (14,16), (28,26), (22,20), (19,21), (25,27), (31,33), (1,3), (3,15), (23,11), (5,17), (21,9), (33,21), (10,8), (17,15), (21,9), (22,10) .

2) Pentru careurile cu caseta libera 4, 6 , 11 si 16 , jocul se poate termina în  36 mutari ale pionului considerând ca acesta se poate deplasa pe orizontala si pe verticala câte o casuta iar atunci când în cale întâlneste un alt pion care are în spate o caseta libera  sare peste acesta iar pionul sarit este capturat.

a) pentru caseta libera cu numarul 4 , mutarile sunt :   

(6,4), (3,5), (16,4), (18,16), (4,6), (6,18), (24,12), (36,24), (15,17), (28,30), (17,29), (21,23), (33,21), (35,33), (13,15), (1,13), (2,14), (15,27), (19,7), (12,10), (10,8), (7,9), (20,8), (33,21), (31,19), (32,20), (30,28), (24,22), (21,23), (19,21),  (23,22), (21,23), (23,22), (28,16), (8,10), (16,4) .

b) pentru caseta libera cu numarul 6 , mutarile sunt :

(18,6), (16,18), (24,12), (6,18), (36,24), (5,17), (23,11), (3,5), (1,3), (5,17), (21,23), (18,16), (15,17), (13,15), (7,9), (9,21), (24,22), (35,23), (23,11), (19,7), (21,23), (33,21), (25,27), (20,8), (7,9), (27,15), (9,21), (31,33), (33,35), (35,29), (28,30), (21,22), (22,24), (30,18), (10,12), (18,6) .

c) pentru caseta libera cu numarul 11 , mutarile sunt :

(9,11), (21,9), (33,21), (3,15), (12,10), (23,11), (24,12), (15,17), (13,15), (21,23), (31,33), (25,27), (6,18), (1,13), (18,16), (5,17), (16,14), (4,16), (13,15), (2,14), (16,18), (29,17), (19,21), (27,29), (35,23), (33,35), (17,29), (36,34), (30,28), (34,22), (21,23), (14,16), (16,17), (18,16), (16,17), (23,11) .

d) pentru caseta libera cu numarul 16 , mutarile sunt :

(4,16), (12,10), (23,11), (24,12), (21,23), (36,24), (24,22), (15,17), (3,15), (19,21), (31,19), (35,23), (21,9), (32,20), (1,3), (3,15), (11,9), (15,3), (7,9), (3,15), (33,21), (22,24), (21,9), (13,15), (15,3), (6,4), (3,5), (19,21), (34,22), (21,23), (23,11), (5,17), (24,18), (12,24), (24,18), (18,16) .

 

Nicu Scutaru:
 S4: (2,4); (14,2);(26,14);(28,26);(25,27);(13,25);(31,19);(22-20);(14,26);(30,28);(18,30); (36,24);(17,29);(35,23);(34;22);(33,21);(32,20);(1,13);(10,8);(2,14);(6,18);(24,12); (21,9);(13,15);(19,21);(5,17);(23,11);(15,3);(3,5);(5,17);(21,23);(23,11);(12,10);(16,4). 

S5:(17,5);(29,17);(21,23);(24,22);(36,24);(27,29);(35,23);(16,28); (34,22);(25,27);(33,21);(13,25);(31,19);(14,26);(32,20); (9,11);(12,10);(24,12);(23,11);(4,16);(6,4);(1,13);(2,14); (12,10);(19,7);(20,8);(7,9);((21,9);(3,15);(22,10);(4,16); (15,17);(17,5). 

S6:(4,6);(16,4);(18,16);(6,18);(22,10);(24,22);(36,24);(35,23);(28,16); (28,16);(24,22);(26,28);(15,27);(28,26);(16,28);(34,22);(25,27);(33,,21); (14,26);(13,25);(32,20);(31,19);(3,15);(21,9);(19,21);(21,23);(1,13); (2,14);(13,15);(15,3);(3,5);(5,17);(23,11);(10,12);(18,6).

 S10:(22,10);(24,22);(36,24);(35,23);(14,16);(2,14);(4,2);(1,3);(20,8);(3,15);(21,9); (23,21);(34,22);(27,15);(25,27);(32,34);(16,28);(34,22);(9,21);(27,15);(13,25); (31,19);(7,9);(9,,21);(22,20);(19,21);(18,16);(10,22);(21,23);(6,18); (5,17);(24,12);(23,11);(12,10). 

S11:(23,11);(35,23);(27,29);(33,35);(30,28);(36,34);(15,17);(13,15); (4,16);(12,10);(24,12);(23,11);(5,17);(21,23);(19,21);(32,20);(31,19); (1,13);(2,14);(16,4);(6,18);(3,5);(23,11);(5,17);(20,22);(9,21);(22,20); (13,15);(19,21);(18,16);(34,22);(15,17);(21,23);(23,11).

 S16:(28-16);(20-22);(33,21);(31,33),(34,32);(32,20);(14,26);(25,27); (30,28);(27,29);(18,30);(36,24);(22,20);(24,22);(35,23);(16,14); (13,15);(1,13);(2,14);(19,7);(6,18);(10,12);(18,16);(22,10);(9,11); (5,17);(23,11);(12,10);(20,8);(7,9);(4,2);(10,8);(2,14);(14,16).