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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?

Lex
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  • I would change the last sentence to a question, to make it clear what the challenge is. – aschepler May 06 '15 at 00:59
  • Would would it mean if the ending were "How can we make 252 predictions with 5 mistakes at most?" As far as I see it there still is a gap of uncertainty or am I wrong? – Lex May 06 '15 at 01:13
  • It works provided you can eliminate untrustworthy meteorologists daily. Making 5 mistakes can guarantee that you can identify the perfect meteorologist, so 252 is a red herring, you could be perfect indefinitely once you have identified the perfect meteorologist. – WW1 May 06 '15 at 01:14
  • It seems like the goal here is to find the always-right meteorologist, effectively "in five tries". (This may-or-may-not mean "in the first five days".) The formulation might be trying to get at a strategy that assumes half of the meteorologists will be wrong at a time. (Maybe they predict by coin flip.) Then, since $30 < 2^5$, firing the wrong predictors whittles the staff down to the always-right predictor. Maybe. (I'm not sure what the significance of the $252$ days is, though.) However, I don't think we know enough about how meteorologists make predictions, or how the weather works. – Blue May 06 '15 at 01:15

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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.

paw88789
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