<|im_start|>system
You are a helpful assistant. You first think about the reasoning process in the mind and then provide the user with the answer. You should try to truely solve the question by yourself without cheating.  <|im_end|>
<|im_start|>user
 A total of  $n$  people compete in a mathematical match which contains  $15$  problems where  $n>12$ . For each problem,  $1$  point is given for a right answer and  $0$  is given for a wrong answer. Analysing each possible situation, we find that if the sum of points every group of  $12$  people get is no less than  $36$ , then there are at least  $3$  people that got the right answer of a certain problem, among the  $n$  people. Find the least possible  $n$ . Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>
<|im_start|>assistant
Let me solve this step by step.
<think>
user
15
A total of  $n$  people compete in a mathematical match which contains  $15$  problems where  $n>12$ . For each problem,  $1$  point is given for a right answer and  $0$  is given for a wrong answer. Analysing each possible situation, we find that if the sum of points every group of  $12$  people get is no less than  $36$ , then there are at least  $3$  people that got the right answer of a certain problem, among the  $n$  people. Find the least possible  $n$ .
test