## Task 1 - 180511

Gerda, Peter, and Renate see a plate of hazelnuts on the table. They do not know how many nuts there are.

Gerda says: "If you take 19 nuts from the plate five times in a row, more than 5 nuts will remain on the plate."

Renate says: "But if you were to take 20 nuts from the plate five times in a row, there would not be enough nuts for that."

Peter says: "One of you two is definitely right."

After counting, it was found that Peter was wrong.

How many nuts were there on the plate in total?
Gerda had meant, due to $5 \cdot 19 + 5 = 100$, that there were more than 100 nuts on the plate. Renate had meant, due to $5 \cdot 20 = 100$, that there were fewer than 100 nuts on the plate. Since Peter was wrong, neither of the girls was right. Therefore, there were exactly 100 nuts on the plate.