Having dinner

Discrete Mathematics Level pending

You and a group of 4 friends are going to a restaurant in a foreign country. There each of you commands one (not necessarily distinct anyway) of the \(m\) types of food available but the staff is foreign and none of you can communicate with it anyway to know what is the name of each meal.

After you command them every of the 5 meals comes and is put in the center of the table. Because the food is good you come again the next days at the restaurant and repeat the same procedure.

Let \(A\) be the maximum value of m for which the group and you can recognize all the available meals in 5 days.

Submit your answer as \(A+1\).

Bonus: Generalize this. That is, what is the minimum number of days necessary given some value of \(m\)?


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