CONCOURS DE PROBLEMES « FFJD 2002 ». Catégorie A.

1 2 3 4 5

11 12 13 14 15

41 42 43 44 45

71 72 73 74 75

1. 27,9,18,33,4(27)36(37A)43(42B)47(48)33,4 + A) (38D)47 + B) (12)47(33C)7(41)38 + C) (18)438(22)14(27)10 +

D) (33)41(328)47 +

2. 28,22,2,25(2)30,40,40 +

3. 41(34)36(50)42(22)31,43,33,1,27(40)22(45)50 +

4. 138,2,26,20,48,5 +

5. 38,38,13,11(2*A)23,4,8(13)24,24 + A) (7)23,4,2 +

6. 11,7,21,31,20,33,5,6 +

7. 23,21(43)278,39,47 +

8. 10,304,8,1,28,27(20A,24)2(29)19(34)30,13(31,30)18(35)45 + A) (19,23)2(29)19(34)30 +

9. 10,350,2,18(12A)32 + A) (40,32)29(37)47 +

10. 34(40*)33(149A)282(8)361(183)18(12*B)29,28,9(23)27(29C)22(17DE,33F)7(12,39)4(43G)12(49)7(21)2(3)24(14)36

(46)250(5)31,35,46 + A) (139)282 + B) (22,24)328(12)27(18)282(183)17 + C) (17)22,3(13)17 + D) (33)31 3 +

E) (34)3(13)17(39)11(20,19,43)16(49)17(44)12 + F) (13,34)7(40)2(45)11(50)6 + G) (44)32(20,50)140(45)183(31)5 +

11. 427,29,28,38,38,2,17 +

12. 393,9,250,40,33,2,29 +

13. 12,5,41,44(50A)28,6 + A) (10)6,28,50 +

14. 22z,4,48(50A)28yx,17,17 + A) (25)1(18)34(22B,50)15,383,20 + B) (29,50)29 + z) 1,32w,4(50) = y) 1(18)37(25)19

(45)23(12)35s(23)13r(7)27(16)272(30)29(7)323(1)383(35)34(40,6)23-28(1)283(6)23-28(1)24(29) = x) 34(17)26t (29,33) = w) 22(167)42v(50)6(17)4u(28) = v) 4(32,34)22(41) = u) 25(23,28,11) = t) 43(24) = s) 382(26)34q(12)339

(30)35(21)28(43)350(38)304(43)24-30(38)293(29) = r) 49(30)43(40)49(23)43(40)32p(40-35) = q) 29(21)328(17)33 (12) 19-23(1)22(30)228(35) = p) 28(49)22(305)34(44)18(39) =

15. 282,10,1(47A)24,6,15(31)42(36)37(10,41)46 + A) (4)293,238,36(10)41(15)37(20)42(25)48 +

Position non justifiée par l’auteur.

16. 182,30,8,28,3(13)26(41)11,37 +

17. 22,31,4,9(6)1(28)44,6 +

18. 293(38A)34,39,2,25 + A) (20)34,39,2,25 +

19. 21z,4,40(453A)2(34B)30,35 + A) (253)2,30,35 + B) (24)35 + z) 28,39(30)4yx(33,44) = y) 5(33,19,34,44) =

x) 7(37)2wv(304,37,34)5(340)46(44) = w) 5(33)46,39(50) = v) 4(19)10u(33)46,39 = u) 31(41)2,36(34) =

20. 44,41,40,1,5,6 +

21. 22,32,27,38(42*A)10,3(43BC)20(49D)20-24,2,30 + A) (43)25,10,3 + B) (20,43)20(48)25/34 + C) (19)21(23)16(29)24,34,7 + D) (48)25/34 +

22. 12(9*)42,15(18 ???)11(23)7(28)2(33)16(339,40)49(45)32(10)4(50)4-10(46)5 +

Justification : 5-9-10-14-18-26-28-36/16-17-21-25-30-41-42-44-48 250(38)…

23. 12zyx,33,3,3x21x8,9,43 + z) 33,14,30(8,13,37)9(42,48)25w(34)13(12)29(40)8,18 = y) 9(223)18(42)183(12)14(47) 250(272,50)15(45)140(350)5(44)9 = x) 8(213)9,8(42)2(12)2-19(33,33)37(48,339)250v(271)27(18) = w) 24(34)13 (12)29(40)8(31) = v) 43(32,327,37) =

24. 14,5,24,48,30,5 +

25. 31zyx,17,39,1(49)40,43,44,44 + z) 17,1(50)23(18A)9,36(26,17)372(21)43(10)27,27(17)1(21)5(49) = A) (45)34(22)

6-1(450)45(26,17)1-18(22-33)29(31)37(42 ???)37(28) = y) 1,19,28,17,23,32(39) = x) 28,19,17,12(11)23(18)17(39) =

26. 9z,493,33,4,8,13,35(30)42(41)37,42 + z) 493,9(16)2(13)4(2)42(41) =

27. 438,5(46)37(23)34(40A)17(45B)161(40)7(44,11C)16(50)161(33)6,17 + A) (44)27(40D)39(45)22(50)17,7 +

B) (44,40)161(45)7 + C) (50)2 + D) (49)45,27 +

28. 10(22A)11,4,41,40,34(38B)49,29 + A) (42)11,4,15,23,48 + B) (40)13z,13x44x48 + z) 13x27x42(47) +

29. 34,30,44,9,4,29,29(25)24 +

30. 27,40,24,34,33(28,18)41(36)417(22)32(41A)28,38,46 + A) (28)23(41)37,42 +

31. 11(13A,128B)482,32,24,31,42,45,9(34)4z(39)27(44)40,49 + A) (21/22)393,2 + B) (11)482(24C)35(128)44,30, 32,44 + C) (127D)44,383,22 + D) (128)35,32,24,24 + z) 3(39)21(11)49(17)450(44) =

32. 32,3z,1(21)20(36/37)47(14/15)6(20,41)29(46)29-23(50)5 + z) 5,1(13)6(31y)282(18,50) = y) (31)282(13)6(18,50) =

33. 44,42,40,2(24A)30,8,20(18)14(23)10(28)5(33)32(39)49 + A) (34)8(12)14(18)9(23)4(28)27(33)43 +

34. 427z,41,31,44y,22,14,19(154)30x(29A)10(19B)4(33)25(39C)10(24)15 + A) (19)10(29)4(33)25 + B) (33)4(19)25(38) 10(24)15 + C) (24)15(29)15-20(34)38(39)49 + z) 28,21,44,40,21(24)17(30)11(34)7(40)2(45)24(50) = y) 14,44,22,3,25

(28)48(33)43(18)19(20)25(24,39)9(22)27 = x) 8(28)10(32)4(37)15(30)47(34)3(39)25(44)39,29(41) =

35. 40,417,28,5(46)23,37(46A)31,41,37 + A) (41)31,36 +

36. 27z,18,21,17,22,40,46(16A)41y(21B)37(27)31 + A) (31)41(16)17 + B) (31)17 +

z) 18,27(31,49,28,16)… y) 17(21)12(27a)8(32)3(38) a) (31)8(37)3(27)20(31)15(36)20(361)47 +

37. 21,327,7(23)1z(34,41)37(17A)46(22)27,41 + A) (32)38,47 + z) 27(35)1(40)21,372(45)28(50)383(45)37(7)31(1)26

(7)272yxw(11)34(16) = y) 271(1) = x) 282,22(1) = w) 34(40)272(21,7) =

38. 24,43,39,29(8,26)20,43(41)47(46)24,24 +

39. 328(43A)21,1,48,25 + A) (21)10,25,1 +

Justification : 5-7-13-17-18-19-23-29-35/10-20-24-27-30-32-33-38-42 15(14)…

40. 18,250,15,4,33,139,17,27 +

41. 21z,31,42,32,5(18A,18)23y,11(33B)7,1(17)6(21)50(27)494(31)40,36 + z) 32,42,21(19)11(14)31(22)26(27) = y) 11(22)7,1x(18,40)10(27) = x) 44(27)24(32)1(40)45(37) = A) (46/30)23/24,28(40)50 + B) (40)7,1(44/45)40,44

42. 482,31,41,393,4,26 +

43. 23,33,44,39,14,2,20,36 +

44. 39,20,27(34A)1,23,25(33)3(18)9(23)14(29)20(34)38(39)49 + A) (21)26,1,25 +

45. 11,13,33,4(34A)21,25(40)39(45)50 + A) (24)21,15 +

46. 427,27,8,2,8,21,17,27 +

47. 23,34,18,32(131A)2,28 + A) (111)32,4,28 +

48. 12,4,10,41,5,5x32x8(12A)7,32 + A) (13)9,33 +

49. 217,18,37,29,2(39ABC)5(6)28(43)28-11,12,48(40)39(45)50 + A) (40)5(45)7,50 + B) (38)5(6)28 + C) (6)5(11,40)11(38)33z,28(45)50(34)12(40)7 + z) 37(43)39,28 +

50. 24(43A)38,23,34,44,427,8(32BCD)3(31EF)20(317)472,31(38)48 + A) (29,29)34(40)504,38… + B) (19)2(23)16 +

C) (20)2(25/32)16 + D) (261)3(32)20 + E) (20,31)20 + F) (19)20(31)20-42(317)26(38)48 +

51. 372,349,10,6(33)1,48(20A)37(194)42(30,34)38(39)49 + A) (24)34(20)25(29)14(33)25(38)48 +

52. 14,20,9,4(36)31(47A)33,36,42 + A) (367)36(31,27)383(282)38,48 +

53. 12z,42,5,13,49(11,11)31 + z) 20,34(31)367 =

54. 28,183,2,15(10,371)467,31,37(22)287,21(18,23)11(29)7(34)2(39)30(44)39,28,32 +

55. 11,2,5,40,44 +

56. 44,24,240,17,7,1(261)29(36)47(32)250(38)24,15,24 +

57. 37,7,250,2,40(35A)34(6)7(11,40)11(45)50 + A) (6)35(34)44 +

58. 43,21,41,30,8,2,48,12 +

59. 43z,5y,30,45(6)7(11,40)11(45)50 + z) 5(30,20)3(25)22(42)182(48) = y) 4,30,22(6) =

60. 22,2,19,3,50,37 +

61. 31,4,30,37(50)39,37 +

62. 23,41,3(10,30)31,31-26(34)43,25 +

Justification : 4-8-13-20-22-26-28-44/15-24-29-31-34-35-40-43-47-49 350(37)…

63. 12,272,12,23,383,12,39(34,34)8(39)3(44,44)40,12(6)7(11,40)11(45)50 +

64. 449,41,33,8,40,2,5 +

65. 10(42)37,4,20,4x39x10,45 +

66. 29,23,3,5(44)28(49A)44,34 + A) (50)6(40,45)1 +

67. 338,11,2,30,16 +

68. 23(29)11,2,38,19,4(32)34,48 +

69. 9,4,34,19,7,2,11(37)28(361,42)37,27 +

70. 24(30*)3,21,40,32(21,10)32(15)37(20)42(25)48 +

71. 12zy,40,1(34)25(393A,24)25-43(42)38,43(29B)39,39 + A) (350)45 + B) (38,29)28(34)44 + z) 1,182,25(350,15) =

y) 417(350)1xw(12,18,23)6(394,50) = x) 19(394)28v(50)22(17)12(28)3(46)39(5) = w) 382(394)30(34,50)22(17) = v) 30(50) =

72. 438zyxw,21v,14,34,22,461u(22)33ts(27A)28rqp(32)37 + A) (37)32 + z) 37(17)38 = y) 21,11(45)428(50)383(45)6

(40)14,1(35)38(23)29(49)1(16)45(41,15) = x) 14(17,22) = w) 428,21,14,34,22,461(22)33(27)38(32,22)37(27) =

v) 14(22,45) = u) 33(37) = t) 32(37) = s) 417(28) = r) 29(32)23(317,46)18 = q) 417(32,37,37) = p) 38(32,22)37(27)

28(32)22 =

Justification : 6-7-8-10-16-28-31-36-40/17-19-21-22-27-33-39-42-43-46-47 11(626)…

73. 23,33,338,41,27,40,10(23)5(29)28(34)44(11,40)11(45)50 +

74. 18z(12A)44,29,42,7,18,4,26(40)17(45)50 + A) (22)4,47(45)41,38,39(50)6(27B)1(32)44(20)28,15 + B) (45)1(27)28 +

z) 44,6,1,42(46)47y(40)15x(45)10(38,5)20(50) = y) 25(40)15(45)10(38)5,14,2 = x) 482(38)25,33(44)36(50)4(17) =

75. 283,24,43,18,449,33,1(40A)29(44)39(50)44(45)1(50)45 + A) (28)29(32B)42(40)15(37)47(44)40,44 + B) (40)38(44)40,44 +

76. 39(44*)28,36(44,50)272,21z,31(36)37,37 + z) 23(11)38(31)42(16)372(7,29)28(18)33(27)29(4)38(15)33(10)32(19) =

77. 33zy(104ABC)7(12)11,7,31,28,3,2 + Guerra A) (15)28,31(11,12)27(138)239(17)32(172)194,3(23)27,204(31)149(36)8

(29,38,41)9-3(46)249(27D)2(272)21(327)32,193 + B) (271)339xwv(15^E)7,18,36(22)32(18)27,27(23)37(28)29(13)14 +

C) (32,27,48)15 + D) (41)2(36)26(20)48(25)39(27)43(31)48 + E) (36)15(14)7(239,7(31F,41)37,10(38)194(27)31(43)2

F) (14)20,2(19,31,41)37,10 + z) 15(14)33(7,20,47) = y) 18(261,21,44)15,13(49)8(7)20u(32)2(21,16,40) = x) 239(27)8

(32)28(15,11,3) = w) 15(36,31,28)32(41)19,243(40) = v) 38,47(104)15(28)32(149,17)10(14,11,3) + u) 2(21,32,37..) +

78. 393,27,38,8,43,37,7(31)2(9,36)26(41)37,24(37)47 +

79. 41,193,33,37 +

80. 294,11,2(46)49z(14)32(46)5 + z) 5(19/14yx) = y) (10)21,35 + x) (28/23)46,17(45)50 +

81. 172,7,21(254A)19,1,20(32)42(9)26(13)48(38)25(19)3(10,43)13,49 + A) (514)9,1,24(32)33(37)47(30)10(34)29,5 +

Position non justifiée par l’auteur.

82. 461,22,42,5,24,24 +

83. 7,44,328,27,3,13,24,45 +

84. 22z,7,35(38)4(12)7,48 + z) 293,18,37(25,240) =

85. 193,3(44)38,6 +

86. 428z,439,493,42,2,30(25)48(140,14)20,350 + z) 19,10(16,37)4y(39,50)44(47)... y) 5(39)46,44(24) =

87. 22,31,34,3,8(40)17(45)261 +

Position non justifiée par l’auteur.

88. 21,42,32,5(18A,18)23z,11(33B)7,1(17)6(21)50(27)494(31)40,36 + z) 11(22)7,1y(18,40)10(27) = y) 44(27)24(32)1(40)45(37) = A) (46/30)23/24,28(40)50 + B) (40)7,1(44/45)40,44

89. 12(18A)7,30,8,4(37)20,31,37 + A) (49)1,27(18,14,24)17,18,13 +

90. 39,19,194,1(36)40,35(42A)21,37 + A) (29)40(42B)21,37 + B) (33)44(42)11,37 +

91. 338,27,9,2,35 +

92. 12,42,43,25,5(28)14(20,38)33(29)14 +

93. 33,4,40(49)43(5)15,46 +

94. 40,41,37,25,1(11,11)21 +

Remerciements à tous les participants ainsi qu’aux membres du jury.

Thank you very much to all the participants and to the members of the jury.

Jury : S.de Bruijn, A.Hlasny, L.de Rooij, S.Yushkevitch, S.Zilevicius.

Participation au concours « FFJD 02 » : 49.

France : 11 Lituanie : 11 Belarus : 6 Pays-Bas : 6 Ukraine : 6 Russie : 4 Italie : 2 Israël : 1 Lettonie : 1 USA : 1

Remarks should be sent before 31-08-2002/Les observations sont à envoyer avant le 31-8-2002 à :