3. A dish contains 100 candies. Juan removes candies from the dish each day and no candies are added to the dish. On day 1, Juan removes 1 candy. On day 2, Juan
removes 2 candies. On each day that follows, Juan removes 1 more candy than he
removed on the previous day. After day n, Juan has removed a total of at least 64
candies. What is the smallest possible value of n?

Please give answers and how to solve it step by step thank you!!!

0.02040816326

there is only one way to arrange all the eight relative to each other because they are not distinct. we have

now there are nine places to place an (and not more than one in one place).   because we have four symbols, we need to choose four of these nine places to insert an . order does not matter because the are not distinct.

thus there are 1 · c(9,4) ways, or, if we calculate it,

thus there are 126 ways to form such "words."