## Task 3 - 070623

After a shooting competition, Elke, Regina, Gerd, and Joachim compared their shooting performances. The following was established:

(1) Joachim scored more rings than Gerd.

(2) Elke and Regina achieved the same total number of rings as Joachim and Gerd together.

(3) Elke and Joachim together scored fewer rings than Regina and Gerd.

Determine the ranking of the shooters in descending order of the number of rings!
If the ring numbers of the shooters are denoted by the initials of their respective first names, then from the contributions of the task we get

(1) $J>G$

(2) $E+R=J+G$

(3) $E+J<G+R$

From (1) and (3), we get $E+J<J+G$, thus $E<G$. From (2), we get $E+R>J+G$, thus $R>J$. Since $J>G$ and $E<G$, it follows that $R>J>G>E$. The sought-after order is: Regina, Joachim, Gerd, Elke.