Q: What is the difference between the sum of the first 2023 even counting mumbers and the sum of the first 2023 odd counting numbers?

A: 2023
If we “solve a simpler problem” (like Polya recommended), we can try the first 10 even counting numbers and the first 10 odd counting numbers.

2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20
1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19

Notice that each of the even numbers in the top row is one more than its corresponding odd number below it. Therefore, the difference between the sum of these rows of numbers is 10.

If we now expand that idea to the first 2023 even numbers vs the first 2023 odd numbers, each of the even numbers is 1 more than its corresponding odd number. Therefore, the difference is 2023.

Click here to see the AMC 12 that inspired this problem