To find a combination of numbers from the set without repetition that adds up to 43,958, we need to carefully select and sum up the largest available numbers.

Approach:

• Start with the largest numbers to reach the total, avoiding any repetition.

Let’s proceed:

1. $5,000$ → Sum: 5,000
2. $4,998$ → Sum: 5,000 + 4,998 = 9,998
3. $4,500$ → Sum: 9,998 + 4,500 = 14,498
4. $4,000$ → Sum: 14,498 + 4,000 = 18,498
5. $3,456$ → Sum: 18,498 + 3,456 = 21,954
6. $2,500$ → Sum: 21,954 + 2,500 = 24,454
7. $2,499$ → Sum: 24,454 + 2,499 = 26,953
8. $1,971$ → Sum: 26,953 + 1,971 = 28,924
9. $1,923$ → Sum: 28,924 + 1,923 = 30,847
10. $1,241$ → Sum: 30,847 + 1,241 = 32,088
11. $1,212$ → Sum: 32,088 + 1,212 = 33,300
12. $1,194$ → Sum: 33,300 + 1,194 = 34,494
13. $1,190$ → Sum: 34,494 + 1,190 = 35,684
14. $1,083$ → Sum: 35,684 + 1,083 = 36,767
15. $1,030$ → Sum: 36,767 + 1,030 = 37,797
16. $1,023$ → Sum: 37,797 + 1,023 = 38,820
17. $966$ → Sum: 38,820 + 966 = 39,786
18. $901$ → Sum: 39,786 + 901 = 40,687
19. $866$ → Sum: 40,687 + 866 = 41,553
20. $761$ → Sum: 41,553 + 761 = 42,314
21. $746$ → Sum: 42,314 + 746 = 43,060
22. $744$ → Sum: 43,060 + 744 = 43,804
23. $154$ → Sum: 43,804 + 154 = 43,958

Thus, the selected combination of values that add up to 43,958 is:

• $5,000, 4,998, 4,500, 4,000, 3,456, 2,500, 2,499, 1,971, 1,923, 1,241, 1,212, 1,194, 1,190, 1,083, 1,030, 1,023, 966, 901, 866, 761, 746, 744, 154$

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:

1. How would you solve the problem if the target sum was a different number, say 50,000?
2. Can you think of a way to approach this problem using programming (e.g., Python)?
3. What would happen if negative numbers were included in the set?
4. How could this problem be solved using a greedy algorithm?
5. How would you find multiple solutions that add up to the target sum?

Tip: When solving similar problems, sorting the numbers in descending order can help minimize the number of values needed to reach the target sum.