Answer:
4 other ways (5 ways, total).
Explanation:
You want to know how many other ways 75 can be written as the sum of consecutive whole numbers other than 24+25+26.
Solution
If 75 is written as the sum of an odd number of integers, the middle integer of the set will be 75 divided by the number of integers. The divisors of 75 are {1, 3, 5, 15, 25, 75}. If the numbers in the sum are non-negative, the number of integers involved cannot be more than √(2·75) ≈ 12. Then allowed odd numbers of integers in the sum are 3 and 5.
If 75 is written as the sum of an even number of integers, the quotient when 75 is divided by the number of integers must be 1/2 more than a whole number. Such integer divisors are 2, 6, and 10.
Sums
37 + 38 = 75 . . . . 2 integers
24 + 25 + 26 = 75 . . . . 3 integers (the given sum)
13 + 14 + 15 + 16 + 17 = 75 . . . . 5 integers
10 + 11 + 12 + 13 + 14 + 15 = 75 . . . . 6 integers
3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 = 75 . . . . 10 integers
There are 4 other ways to use consecutive non-negative integers to make a sum of 75.