Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# Problem B. 4222. (December 2009)

B. 4222. The students in a class of 30 organized 16 trips during the school year. Eight students went on the trip each time in a van. Show that there are two students in the class who went on at least two trips together.

(3 pont)

Deadline expired on January 11, 2010.

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

Megoldás. Az osztály diákjaiból $\displaystyle {30\choose 2}=435$ párt képezhetünk. Minden egyes kiránduláson $\displaystyle {8\choose 2}=28$ pár vett részt. A 16 kirándulásra számítva ez $\displaystyle 16\cdot 28=448$ pár, tehát kell legyen olyan pár, amelyik két kiránduláson is részt vett.

### Statistics:

 132 students sent a solution. 3 points: 92 students. 2 points: 13 students. 1 point: 4 students. 0 point: 20 students. Unfair, not evaluated: 3 solutions.

Problems in Mathematics of KöMaL, December 2009