## Task 1 - 320711

Karsten, Lutz, Mike, and Norbert collected mushrooms. Afterwards, they compared their collection results and found:

(1) Norbert collected more than Mike.

(2) Karsten and Lutz together collected as much as Mike and Lutz together.

(3) Karsten and Norbert together collected less than Lutz and Mike together.

Investigate whether from these statements:

a) exactly one of the four boys can be identified as the one who collected the most mushrooms,

b) exactly one of the four boys can be identified as the one who collected the fewest mushrooms!

Give the name of the respective boy, if that is the case!
For the collection results $K, L, M, N$ of Karsten, Lutz, Mike, and Norbert respectively, the following can be derived from the given information: 

After (1) it follows that $N>M$. (4)

After (2) it follows that $K+L=M+L$, thus $K=M$. (5) After (3) it follows that $K+N>N>M=K$, which is shown:

a) From the given information, only Lutz stands out as the collector of the most mushrooms.

b) From the given information, it is not exactly one of the four boys who stands out as the collector of the fewest mushrooms (but rather each of the two boys, Mike and Karsten).