There are 30 metereologists working in their laboratory making predictions about the weather for the next day. They say either "Tomorrow will be sunny" or "Tomorrow will be cloudy". One of the metereologists is always right. Others might make a mistake. We need to make predictions for 252 days making no more than 5 mistakes.
Do you think the formulation of the problem is informative so that the puzzle can be solved?
Always forecast according to the majority prediction (or if there is a tie for sunny and cloudy predictions, forecast randomly). Anytime the majority is correct, you haven't used one of your five failures. Anytime the majority is wrong, you get to fire at least half the remaining meteorologists. So in five wrong forecasts, in the worst case, the number of remaining meteorologists will be $15$ (after wrong forecast 1), $7, 3, 1$. So actually, after four wrong forecasts, you should be down to the one always-right meteorologist.