Problem K. 795. (January 2024)

K. 795. The product of four distinct positive prime numbers is \(\displaystyle n\). Find the number of different rectangular prisms that can be created using \(\displaystyle n\) identical little cubes.

(5 pont)

Deadline expired on February 12, 2024.

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

Megoldás. Mivel a négy prím különböző, ezért 14-félét. (\(\displaystyle n=pqrs\).)

\(\displaystyle 1\times1\times pqrs\), \(\displaystyle 1\times p\times qrs\), \(\displaystyle 1\times q\times prs\), \(\displaystyle 1\times r\times pqs\), \(\displaystyle 1\times s\times pqr\), \(\displaystyle 1\times pq\times rs\), \(\displaystyle 1\times pr\times qs\), \(\displaystyle 1\times ps\times qr\), \(\displaystyle p\times q\times rs\), \(\displaystyle p\times r\times qs\), \(\displaystyle p\times s\times qr\), \(\displaystyle q\times r\times ps\), \(\displaystyle q\times s\times pr\), \(\displaystyle r\times s\times pq\).

Statistics:

91 students sent a solution.
5 points:	Csabai Samu, Farkas Simon, Hajnal Ákos Huba, Ivák László, Juhász Gergely, Juhász Zsombor, Károly Kamilla , Máté Kristóf, Olajos Anna, Pázmándi Renáta , Pivárcsik Márk, Schmidt Marcell, Szabó Máté, Szabó Medárd, Válek Péter, Viczián Adél.
4 points:	Bubálik Nóra, Chen Peidong, Li Yujin, Ördög Dominik, Szalóki Árpád, Szedmák Szabrina.
3 points:	4 students.
2 points:	17 students.
1 point:	6 students.
0 point:	2 students.
Not shown because of missing birth date or parental permission:	40 solutions.

Problems in Mathematics of KöMaL, January 2024