## Task 1 - 150811

Peter came back from shopping. He shopped in exactly 4 stores and had exactly $35 \mathrm{M}$ available for this. He returned exactly $2 \mathrm{M}$ to his mother and reported:

"In the vegetable store, I paid $4 \mathrm{M}$ and a bit more, certainly more than 10 Pf. In the stationery store, I had to pay more than in the vegetable store, it was an even number of Pfennigs and no 5-Pfennig piece was involved. At the bakery, it was more than in the vegetable and stationery stores combined, but this amount of money was odd, and at the consumer goods store, I finally paid more than in the other three stores combined."

What amounts of money did Peter pay in the four mentioned stores?
Peter must have paid at least 4.11 M in the vegetable store. If he had paid 4.12 M or more, he would have paid 4.13 M or more in the stationery store, 8.26 M or more at the bakery, 16.52 M or more at the grocery store, a total of 33.03 M or more, and thus could have brought back at most 1.97 M. Therefore, he paid exactly 4.11 M in the vegetable store.

In the stationery store, he consequently had to pay at least 4.12 M. However, he could not have paid 4.14 M or more; for otherwise, he would have paid 8.26 M or more at the bakery and 16.52 M or more at the grocery store, a total of 33.03 M or more, which is not possible.

Therefore, he paid exactly 4.12 M in the stationery store. At the bakery, he then had to pay at least 8.25 M according to the problem. However, he could not have paid 8.27 M or more; for in this case, he would have paid 16.51 M or more at the grocery store, a total of 33.01 M or more, which is also not possible.

Therefore, he paid exactly 8.25 M at the bakery. Since 4.11 M + 4.12 M + 8.25 M = 16.48 M and Peter brought back exactly 2.00 M, he paid exactly 16.52 M at the grocery store.