Не используя скобок, вырази число 30 с помощью цифр от 1 до 5 включительно. Цифры расположи в порядке возрастания.

Решение:

Нужно составить число 30, используя цифры 1, 2, 3, 4, 5, расположенные в порядке возрастания, без использования скобок.

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

Ответ: \( 1 + 2 + 3 + 4 \times 5 = 30 \).