ЯсноПонятно24

Сначала составим все возможные множества из 5 различных натуральных чисел, где каждое число меньше 11 и сумма любых двух чисел не равна 11:

1. {1, 2, 3, 4, 5}
2. {1, 2, 3, 4, 6}
3. {1, 2, 3, 4, 7}
4. {1, 2, 3, 4, 8}
5. {1, 2, 3, 4, 9}
6. {1, 2, 3, 5, 6}
7. {1, 2, 3, 5, 7}
8. {1, 2, 3, 5, 8}
9. {1, 2, 3, 5, 9}
10. {1, 2, 3, 6, 7}
11. {1, 2, 3, 6, 8}
12. {1, 2, 3, 6, 9}
13. {1, 2, 3, 7, 8}
14. {1, 2, 3, 7, 9}
15. {1, 2, 3, 8, 9}
16. {1, 2, 4, 5, 6}
17. {1, 2, 4, 5, 7}
18. {1, 2, 4, 5, 8}
19. {1, 2, 4, 5, 9}
20. {1, 2, 4, 6, 7}
21. {1, 2, 4, 6, 8}
22. {1, 2, 4, 6, 9}
23. {1, 2, 4, 7, 8}
24. {1, 2, 4, 7, 9}
25. {1, 2, 4, 8, 9}
26. {1, 2, 5, 6, 7}
27. {1, 2, 5, 6, 8}
28. {1, 2, 5, 6, 9}
29. {1, 2, 5, 7, 8}
30. {1, 2, 5, 7, 9}
31. {1, 2, 5, 8, 9}
32. {1, 2, 6, 7, 8}
33. {1, 2, 6, 7, 9}
34. {1, 2, 6, 8, 9}
35. {1, 2, 7, 8, 9}
36. {1, 3, 4, 5, 6}
37. {1, 3, 4, 5, 7}
38. {1, 3, 4, 5, 8}
39. {1, 3, 4, 5, 9}
40. {1, 3, 4, 6, 7}
41. {1, 3, 4, 6, 8}
42. {1, 3, 4, 6, 9}
43. {1, 3, 4, 7, 8}
44. {1, 3, 4, 7, 9}
45. {1, 3, 4, 8, 9}
46. {1, 3, 5, 6, 7}
47. {1, 3, 5, 6, 8}
48. {1, 3, 5, 6, 9}
49. {1, 3, 5, 7, 8}
50. {1, 3, 5, 7, 9}
51. {1, 3, 5, 8, 9}
52. {1, 3, 6, 7, 8}
53. {1, 3, 6, 7, 9}
54. {1, 3, 6, 8, 9}
55. {1, 3, 7, 8, 9}
56. {1, 4, 5, 6, 7}
57. {1, 4, 5, 6, 8}
58. {1, 4, 5, 6, 9}
59. {1, 4, 5, 7, 8}
60. {1, 4, 5, 7, 9}
61. {1, 4, 5, 8, 9}
62. {1, 4, 6, 7, 8}
63. {1, 4, 6, 7, 9}
64. {1, 4, 6, 8, 9}
65. {1, 4, 7, 8, 9}
66. {1, 5, 6, 7, 8}
67. {1, 5, 6, 7, 9}
68. {1, 5, 6, 8, 9}
69. {1, 5, 7, 8, 9}
70. {1, 6, 7, 8, 9}
71. {2, 3, 4, 5, 6}
72. {2, 3, 4, 5, 7}
73. {2, 3, 4, 5, 8}
74. {2, 3, 4, 5, 9}
75. {2, 3, 4, 6, 7}
76. {2, 3, 4, 6, 8}
77. {2, 3, 4, 6, 9}
78. {2, 3, 4, 7, 8}
79. {2, 3, 4, 7, 9}
80. {2, 3, 4, 8, 9}
81. {2, 3, 5, 6, 7}
82. {2, 3, 5, 6, 8}
83. {2, 3, 5, 6, 9}
84. {2, 3, 5, 7, 8}
85. {2, 3, 5, 7, 9}
86. {2, 3, 5, 8, 9}
87. {2, 3, 6, 7, 8}
88. {2, 3, 6, 7, 9}
89. {2, 3, 6, 8, 9}
90. {2, 3, 7, 8, 9}
91. {2, 4, 5, 6, 7}
92. {2, 4, 5, 6, 8}
93. {2, 4, 5, 6, 9}
94. {2, 4, 5, 7, 8}
95. {2, 4, 5, 7, 9}
96. {2, 4, 5, 8, 9}
97. {2, 4, 6, 7, 8}
98. {2, 4, 6, 7, 9}
99. {2, 4, 6, 8, 9}
100. {2, 4, 7, 8, 9}
101. {2, 5, 6, 7, 8}
102. {2, 5, 6, 7, 9}
103. {2, 5, 6, 8, 9}
104. {2, 5, 7, 8, 9}
105. {2, 6, 7, 8, 9}
106. {3, 4, 5, 6, 7}
107. {3, 4, 5, 6, 8}
108. {3, 4, 5, 6, 9}
109. {3, 4, 5, 7, 8}
110. {3, 4, 5, 7, 9}
111. {3, 4, 5, 8, 9}
112. {3, 4, 6, 7, 8}
113. {3, 4, 6, 7, 9}
114. {3, 4, 6, 8, 9}
115. {3, 4, 7, 8, 9}
116. {3, 5, 6, 7, 8}
117. {3, 5, 6, 7, 9}
118. {3, 5, 6, 8, 9}
119. {3, 5, 7, 8, 9}
120. {3, 6, 7, 8, 9}
121. {4, 5, 6, 7, 8}
122. {4, 5, 6, 7, 9}
123. {4, 5, 6, 8, 9}
124. {4, 5, 7, 8, 9}
125. {4, 6, 7, 8, 9}
126. {5, 6, 7, 8, 9}

Теперь вычислим произведение каждого множества и сложим все результаты:

12345 = 120 12346 = 144 12347 = 168 12348 = 192 12349 = 216 12356 = 180 12357 = 210 12358 = 240 12359 = 270 12367 = 252 12368 = 288 12369 = 324 12378 = 336 12379 = 378 12389 = 432 12456 = 240 12457 = 280 12458 = 320 12459 = 360 12467 = 336 12468 = 384 12469 = 432 12478 = 448 12479 = 504 12489 = 576 12567 = 420 12568 = 480 12569 = 540 12578 = 560 12579 = 630 12589 = 720 12678 = 672 12679 = 756 12689 = 864 12789 = 1008 13456 = 360 13457 = 420 13458 = 480 13459 = 540 13467 = 504 13468 = 576 13469 = 648 13478 = 672 13479 = 756 13489 = 864 13567 = 630 13568 = 720 13569 = 810 13578 = 840 13579 = 945 13589 = 1080 13678 = 1008 13679 = 1134 13689 = 1296 13789 = 1512 14567 = 840 14568 = 960 14569 = 1080 14578 = 1120 14579 = 1260 14589 = 1440 14678 = 1344 14679 = 1512 14689 = 1728 14789 = 2016 15678 = 1680 15679 = 1890 15689 = 2160 15789 = 2520 16789 = 3024 23456 = 720 23457 = 840 23458 = 960 23459 = 1080 23467 = 1008 23468 = 1152 23469 = 1296 23478 = 1344 23479 = 1512 23489 = 1728 23567 = 1260 23568 = 1440 23569 = 1620 23578 = 1680 23579 = 1890 23589 = 2160 23678 = 2016 23679 = 2268 23689 = 2592 23789 = 3024 24567 = 1680 24568 = 1920 24569 = 2160 24578 = 2240 24579 = 2520 24589 = 2880 24678 = 2688 24679 = 3024 24689 = 3456 24789 = 4032 25678 = 3360 25679 = 3780 25689 = 4320 25789 = 5040 26789 = 6048 34567 = 2520 34568 = 2880 34569 = 3240 34578 = 3360 34579 = 3780 34589 = 4320 34678 = 4032 34679 = 4536 34689 = 5184 34789 = 6048 35678 = 5040 35679 = 5670 35689 = 6480 35789 = 7560 36789 = 9072 45678 = 6720 45679 = 7560 45689 = 8640 45789 = 10080 46789 = 12096 56789 = 15120

Сложим все полученные произведения:

120 + 144 + 168 + 192 + 216 + 180 + 210 + 240 + 270 + 252 + 288 + 324 + 336 + 378 + 432 + 240 + 280 + 320 + 360 + 336 + 384 + 432 + 448 + 504 + 576 + 420 + 480 + 540 + 560 + 630 + 720 + 672 + 756 + 864 + 1008 + 360 + 420 + 480 + 540 + 504 + 576 + 648 + 672 + 756 + 864 + 630 + 720 + 810 + 840