<|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
 Neznayka, Doctor Pilyulkin, Knopochka, Vintik, and Znayka participated in a math contest. Exactly four out of them solved each problem. Znayka solved more problems than each of the others - 10 problems, while Neznayka solved fewer problems than each of the others - 6 problems. How many problems in total were there in the math contest? 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
10
Neznayka, Doctor Pilyulkin, Knopochka, Vintik, and Znayka participated in a math contest. Exactly four out of them solved each problem. Znayka solved more problems than each of the others - 10 problems, while Neznayka solved fewer problems than each of the others - 6 problems. How many problems in total were there in the math contest?
test