Joan has 100 candies to distribute among 10 children. if each child receives at least 1 candy and no two children receive the same number of candies, what is the maximum number of candies that a child can receive?

The best way to determine the maximum number of candies that a child can have is to assume that the other children will be receiving the lowest number of candies possible considering that there should be no repetitions in the number of candies.

The 9 other children will be receiving: 1, 2, 3, 4, 5, 6, 7, 8, 9. These numbers totaled 45. Then, we subtract the calculated value from the total pieces of candies to determine the answer.

n = 100 - 45

Hence, the answer is 55.