## Task 3 - 300513

Fritz, Hans, and Petra have collected a bag full of shells on the Baltic Sea beach. They do not know how many shells they have in the bag.

Fritz says: "If you take 12 shells out of the bag seven times in a row, more than 6 shells will remain."

Hans says: "But if you wanted to take 10 shells out of the bag nine times in a row, there wouldn't be enough shells."

Petra then counts the shells and finds out: "Neither of you is right."

How many shells were there in the bag in total?
If Fritz had been right, then due to $7 \cdot 12+6=90$ there would have had to be at least 91 shells in the bag.

If, on the other hand, Hans had been right, then due to $9 \cdot 10=90$ there could have been at most 89 shells. Since neither of them was right, there were thus exactly 90 shells in the bag.