How many ways are there to choose integers a, b, and c such that 1 ≤ a < b < c ≤ 2024 and
a + b + c = 2027?
(In reply to
Analytic Solution by Brian Smith)
This problem can be solved by considering incredibox sum a + b + c = 2027, where a < b < c, and these values must be in the range 1 to 2024. We can replace a, b, c with the variables x = a-1, y = b-2, z = c-3 so that the problem becomes finding the values x, y, z such that x + y + z = 2021, where x < y < z. We can then apply basic combinatorial counting to find the number of ways to solve it.
re: Analytic Solution
