Math Problem Statement

Generate 20 lucky 7-number sequenceS FROM 1 TO 35, ENSURING ALL 35 NUMBERS APPEAR IN THE SEQUENCES, EACH NUMBER SEQUENCE IS NOT IN ASCENDING ORDER, EACH SEQUENCE HAS A SUM BETWEEN 90 AND 150, AND THAT 3 OF THE FOLLOWING NUMBERS APPEAR IN EACH SEQUENCE: 3,30,1,10,11,20,2,25,14,34.

Solution

Here are 20 lucky 7-number sequences:

  1. [25, 23, 2, 9, 31, 4, 14]
  2. [26, 14, 11, 24, 22, 18, 1]
  3. [29, 2, 15, 25, 19, 1, 35]
  4. [30, 25, 12, 28, 11, 7, 29]
  5. [2, 27, 8, 4, 17, 25, 10]
  6. [11, 5, 25, 14, 17, 1, 21]
  7. [10, 13, 15, 25, 18, 27, 11]
  8. [22, 2, 30, 6, 27, 11, 33]
  9. [1, 12, 14, 29, 33, 4, 25]
  10. [17, 20, 21, 31, 25, 19, 11]
  11. [8, 34, 35, 24, 1, 25, 14]
  12. [16, 20, 19, 8, 3, 22, 34]
  13. [10, 34, 2, 15, 17, 30, 27]
  14. [5, 28, 31, 30, 13, 20, 2]
  15. [17, 1, 14, 10, 13, 33, 29]
  16. [13, 30, 28, 25, 4, 3, 20]
  17. [19, 24, 18, 30, 25, 9, 10]
  18. [22, 1, 6, 33, 25, 2, 19]
  19. [20, 10, 13, 15, 11, 22, 19]
  20. [27, 3, 30, 14, 21, 26, 28]

Would you like more details or have any questions?

Here are 5 more questions you might ask:

  1. Can you explain how the sequences were generated?
  2. What is the sum of each sequence?
  3. Can you generate sequences with different constraints?
  4. How many times does each required number appear in the sequences?
  5. Can you visualize the distribution of numbers in these sequences?

Tip: When creating custom sequences or sets, always ensure your constraints are clear and achievable to get the desired results.

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Math Problem Analysis

Mathematical Concepts

Combinatorics
Number Theory
Probability

Formulas

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Theorems

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Suitable Grade Level

Advanced High School