Problem K. 729. (September 2022)

K. 729. What angle is enclosed by the hands of the tower hall clock 2022 minutes before it strikes midnight?

(Based on the idea of K.A. Kozma, Győr)

(5 pont)

Deadline expired on October 10, 2022.

Sorry, the solution is available only in Hungarian. Google translation

Megoldás. A nagymutató elfordulása percenként 6 fok (60 perc alatt fordul el 360 fokot), a kismutató elfordulása pedig percenként 0,5 fok (720 perc alatt fordul 360 fokot). Mivel \(\displaystyle 2022\cdot6=12\,132=33\cdot360+252\) és \(\displaystyle 2022\cdot0,5=1011=2\cdot360+291\), ezért a két mutató \(\displaystyle 291-252=39\) fokot zár be egymással.

Statistics:

149 students sent a solution.
5 points:	78 students.
4 points:	7 students.
3 points:	18 students.
2 points:	10 students.
1 point:	6 students.
0 point:	1 student.
Unfair, not evaluated:	18 solutionss.
Not shown because of missing birth date or parental permission:	11 solutions.

Problems in Mathematics of KöMaL, September 2022