## Task 3 - 310613

Elke, Regina, Gerd, and Joachim are comparing their stamp collections. They notice:

(1) Joachim has more stamps than Gerd.

(2) Elke and Regina together have exactly as many stamps as Joachim and Gerd together.

(3) Elke and Joachim together have fewer stamps than Regina and Gerd together.

Determine whether these statements can only be satisfied by one specific order of the number of stamps Elke, Regina, Gerd, and Joachim have!

If this is the case, determine this order, sorted in descending numbers!
Let $E, R, G, J$ denote the number of stamps owned by Elke, Regina, Gerd, and Joachim, respectively. From the given information, we have

$$
J>G, \quad \text { (1) } \quad E+R=J+G, \quad(2) \quad E+J>J+G, \quad(3) \quad R>G, \quad(4) \quad R>J. \quad(5)
$$

From (3), we get $E>G$. Combining this with (1), we have $E>J>G$. Since (5) holds, together with (5), (1), and (4), it is shown that the given information can only be satisfied by the order $R>J>G>E$.