To make the numbers $39, 32, 11, 24, 13$ equal 109, one method is to sum a selection of them. Let's check the combinations to see if a subset or a combination of operations can produce 109.

Approach:

• First, try adding them up in different combinations:

1. $39 + 32 + 11 + 24 + 13 = 119$, which is too large.
2. $39 + 32 + 11 + 13 = 95$
3. $32 + 11 + 24 + 13 = 80$
4. $39 + 32 + 24 = 95$
5. $39 + 32 + 13 = 84$
6. $39 + 32 = 71$

Modified approach: Adding operations

Let's combine addition and subtraction:

1. $39 + 32 + 24 + 13 - 11 = 109$

Thus, by adding 39, 32, 24, and 13 and subtracting 11, you get 109.

Would you like more details or explanations?

Here are 5 related questions:

1. How would you solve this problem if only addition was allowed?
2. Can you find a combination of these numbers to equal a different sum, like 100?
3. How could multiplication or division be used in this case?
4. What if we added a new number to this set—what would be a useful number to achieve 109 easily?
5. Can you prove that there are no other combinations that result in 109?

Tip: When working with number combinations, try both addition and subtraction to achieve desired results efficiently.