Like that will ever happen!

Probability Level 3

There are n+mn+m coins in a bag. In the bag nn of them are fair (equal probability of outcomes) and mm of them are double sided heads (heads on both sides).

The probability of picking a random coin and tossing it and getting heads is 1117\frac{11}{17}. Given that nn and mm are positive and that 2n133+m2n\le133+m work out how many different amounts of coins there could be.

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