To achieve a sum of three equal groups from the numbers provided, we will need to find a combination of values that adds up to one-third of the total sum of the provided list. Let's break it down step by step:

Step 1: Calculate the Total Sum of the Provided Numbers

First, we'll sum up all the numbers you gave. After calculating this total, we can determine if it's divisible by 3, and if so, we will try to divide the total sum into three equal parts.

Step 2: Divide the Total by 3

If the sum is divisible by 3, we can attempt to group the numbers into three parts that each sum up to one-third of the total.

Let me first calculate the total sum of the provided numbers and see if it is divisible by 3. List of provided numbers numbers = [ 72500, 85000, 80000, 82000, 83000, 76500, 73500, 85000, 76500, 76500, 82000, 76500, 81000, 76500, 76500, 76500, 78500, 76500, 92000, 85000, 76500, 89000, 82000, 76500, 76500, 85000, 82000, 76500, 164800, 76500, 164000, 76500, 67500, 76500, 161600, 74500, 76500, 76500, 85000, 87500, 76500, 76500, 82000, 79000, 80000, 76500, 76500, 76500, 76500, 78000, 76500, 164000, 76500, 97000, 99500, 82000, 78000, 98500, 86000, 82000, 76500, 76500, 83000, 83500, 76500, 89000, 76500, 82000, 76500, 76500, 88500, 76500, 76500, 76500, 76500, 82000, 76500, 82000 ]

Calculate total sum of numbers

total_sum = sum(numbers) total_sumThe total sum of the numbers you provided is 6,572,400.

Step 1: Check if the total sum is divisible by 3

To split this into three equal groups, we need to check if it is divisible by 3.

Dividing the total sum by 3: $\frac{6572400}{3} = 2190800$ So, each group should sum up to 2,190,800.

Step 2: Grouping the numbers

Next, we will attempt to find three groups of numbers that each add up to 2,190,800. This is a variation of the subset sum problem, which can be computationally complex. Would you like me to attempt finding the combinations for you, or do you have any specific conditions for how you'd like the numbers grouped (e.g., limits on how many numbers can be in each group)?