Рассмотрим все возможные множества из 5 натуральных чисел, где каждое число меньше 11, а сумма любых двух чисел не равна 11. В каждом множестве вычислили произведение всех чисел, а затем все результаты сложили. Чему оказалась равна сумма?

Сначала определим все возможные комбинации из 5 натуральных чисел, каждое из которых 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 найдем произведение каждого из этих множеств и сложим все результаты:

1. 12345 = 120
2. 12346 = 144
3. 12347 = 168
4. 12348 = 192
5. 12349 = 216
6. 12356 = 180
7. 12357 = 210
8. 12358 = 240
9. 12359 = 270
10. 12367 = 252
11. 12368 = 288
12. 12369 = 324
13. 12378 = 336
14. 12379 = 378
15. 12389 = 432
16. 12456 = 240
17. 12457 = 280
18. 12458 = 320
19. 12459 = 360
20. 12467 = 336
21. 12468 = 384
22. 12469 = 432
23. 12478 = 448
24. 12479 = 504
25. 12489 = 576
26. 12567 = 420
27. 12568 = 480
28. 12569 = 540
29. 12578 = 560
30. 12579 = 630
31. 12589 = 720
32. 12678 = 672
33. 12679 = 756
34. 12689 = 864
35. 12789 = 1008
36. 13456 = 360
37. 13457 = 420
38. 13458 = 480
39. 13459 = 540
40. 13467 = 504
41. 13468 = 576
42. 13469 = 648
43. 13478 = 672
44. 13479 = 756
45. 13489 = 864
46. 13567 = 630
47. 13568 = 720
48. 13569 = 810
49. 13578 = 840
50. 13579 = 945
51. 13589 = 1080
52. 13678 = 1008
53. 13679 = 1134
54. 13689 = 1296
55. 13789 = 1512
56. 14567 = 840
57. 14568 = 960
58. 14569 = 1080
59. 14578 = 1120
60. 14579 = 1260
61. 14589 = 1440
62. 14678 = 1344
63. 14679 = 1512
64. 14689 = 1728
65. 14789 = 2016
66. 15678 = 1680
67. 15679 = 1890
68. 15689 = 2160
69. 15789 = 2520
70. 16789 = 3024
71. 23456 = 720
72. 23457 = 840
73. 23458 = 960
74. 23459 = 1080
75. 23467 = 1008
76. 23468 = 1152
77. 23469 = 1296
78. 23478 = 1344
79. 23479 = 1512
80. 23489 = 1728
81. 23567 = 1260
82. 23568 = 1440
83. 23569 = 1620
84. 23578 = 1680
85. 23579 = 1890
86. 23589 = 2160
87. 23678 = 2016
88. 23679 = 2268
89. 23689 = 2592
90. 23789 = 3024
91. 24567 = 1680
92. 24568 = 1920
93. 24569 = 2160
94. 24578 = 2240
95. 24579 = 2520
96. 24589 = 2880
97. 24678 = 2688
98. 24679 = 3024
99. 24689 = 3456
100. 24789 = 4032
101. 25678 = 3360
102. 25679 = 3780
103. 25689 = 4320
104. 25789 = 5040
105. 26789 = 6048
106. 34567 = 2520
107. 34568 = 2880
108. 34569 = 3240
109. 34578 = 3360
110. 34579 = 3780
111. 34589 = 4320
112. 34678 = 4032
113. 34679 = 4536
114. 3