Fox and Ford mushroomed. Totally they picked 30 mushrooms — slippery jacks and birch mushrooms. It is known that among any 14 mushrooms there is at least one slippery jack, and among any 18 mushrooms — at least one birch mushroom. How many slippery jacks did they gather?

241
Among any 14 at least one slippery jack, means: 14 - 1 = 13, that is birch mushrooms no more than 13 among any 18 at least of one birch mushrooms 18-1=17, that is butter no more than 17 only 30, means: 13 birch mushrooms and 17 slippery jacks. Answer: 17 slippery jacks.
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Answer add