Ivana, Majka, Lucka, Saša, and Zuzka competed in reading the same book. In one hour, Lucka managed to read 32 pages, which was exactly halfway between the number of pages read by Saša and Zuzka. Ivana read 5 pages more than Zuzka, and Majka read 8 pages less than Saša. Ivana's result was exactly halfway between Majka's and Zuzka's.

Determine how many pages each of the girls read.

(M. Dillingerová)
Let's consider which of the following possibilities could have occurred: either Sasha read fewer pages than Zuzka, or the opposite. If Sasha had read fewer pages than Zuzka, it would mean that Ivana read the most. However, this would mean that her performance was not halfway between any two girls. Therefore, Zuzka must have read fewer pages than Sasha.

Ivana read 5 more pages than Zuzka, and her result was halfway between Zuzka and Majka. Therefore, Majka read 5 more pages than Ivana, and from the problem statement, we know that Sasha read 8 more pages than Majka. By summing the differences between these four girls, we find that Sasha read $5+5+8=18$ more pages than Zuzka.

![](https://cdn.mathpix.com/cropped/2024_04_17_34e74d7fbf05812a3280g-1.jpg?height=111&width=1082&top_left_y=2320&top_left_x=493)

Lucka read 32 pages, which was halfway between Zuzka and Sasha. Therefore, Zuzka read $32-9=23$ pages, and Sasha read $32+9=41$ pages. From this, we can calculate the other results: Majka read $41-8=33$ pages, and Ivana read $23+5=28$ pages.

Evaluation. 2 points for explaining that Sasha read more than Zuzka; 2 points for explaining that the difference between them was $18; 2$ points for the results of the girls.