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 $n$ ?
3. After 10 days, Juan has removed $1+2+3+4+5+6+7+8+9+10=55$ candies.
On day 11, Juan removes 11 candies so has now removed $55+11=66$ candies.
This means that, after day 10, Juan has removed fewer than 64 candies, and, after day 11, Juan has removed more than 64 candies.
Therefore, the smallest possible value of $n$ is 11 .
ANSWER: 11