To find the combination of numbers from the list that add up closest to 1679, I'll test combinations of the numbers to see which one comes closest to this total.

Here’s the list of numbers you provided:

• 65.00, 150.00, 150.00, 95.00, 150.00, 125.00, 120.00, 99.00, 80.00, 85.00, 160.00, 128.00, 90.00, 220.00, 105.00, 220.00, 80.00, 115.00, 65.00, 105.00, 115.00, 115.00, 95.00, 193.00, 40.00, 145.00, 115.00, 133.27

Let's work through this and find the best combination.

I'll start by checking sums of smaller subsets to zero in on the closest match.

Result: I will calculate and return the closest sum now. itertools

List of numbers provided

numbers = [ 65.00, 150.00, 150.00, 95.00, 150.00, 125.00, 120.00, 99.00, 80.00, 85.00, 160.00, 128.00, 90.00, 220.00, 105.00, 220.00, 80.00, 115.00, 65.00, 105.00, 115.00, 115.00, 95.00, 193.00, 40.00, 145.00, 115.00, 133.27 ]

target_sum = 1679

Find all combinations of numbers

closest_sum = None closest_combination = None

for r in range(1, len(numbers) + 1): for combination in itertools.combinations(numbers, r): current_sum = sum(combination) if closest_sum is None or abs(target_sum - current_sum) < abs(target_sum - closest_sum): closest_sum = current_sum closest_combination = combination

closest_sum, closest_combinationIt seems that the search for the closest combination of numbers was too computationally intense. Instead of checking all possible combinations, I'll try a more efficient approach by using a greedy method or narrowing down the search space.

Let me try again to find a combination that adds up closest to 1679. Greedy approach to find the combination closest to the target sum (1679)

Sort the numbers in descending order to check larger numbers first

sorted_numbers = sorted(numbers, reverse=True)

Attempt to reach the target sum by adding the largest possible numbers

current_sum = 0 chosen_numbers = []

for num in sorted_numbers: if current_sum + num <= target_sum: chosen_numbers.append(num) current_sum += num

Final closest sum and chosen numbers

current_sum, chosen_numbersThe closest sum I found to 1679 is 1649.27, using the following combination of numbers:

• 220.00, 220.00, 193.00, 160.00, 150.00, 150.00, 150.00, 145.00, 133.27, 128.00

This combination is only 29.73 short of the target.

Would you like to explore more combinations, or need further clarification?

Here are some related questions you might find interesting:

1. How can I find the closest sum using dynamic programming?
2. How can I handle this problem efficiently when there are many numbers?
3. What other techniques can be used for similar "subset sum" problems?
4. How can I improve this approach for larger sets of numbers?
5. What are the real-world applications of finding closest sums like this?

Tip: When dealing with large lists, sorting the numbers first can sometimes make it easier to find good solutions quickly by focusing on the larger numbers first.