Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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Problem C. 875. (December 2006)

C. 875. There are two kind of rolls sold in Hungary, their prices are 15 forints and 12 forints, respectively. (Forint is the Hungarian currency, HUF.) We buy some of each. a) Is it possible that we pay 500 forints? b) Is it possible that we pay 600 forints?

(5 pont)

Deadline expired on January 15, 2007.


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

Megoldás. Mivel 15 és 12 egyaránt osztható 3-mal, ezért a vásárlás összege is osztható 3-mal. 500 Ft-ért tehát nem vásárolhattunk. 600 Ft-ért igen, ha a zsömlék száma osztható 4-gyel (ekkor a kiflik száma oszható 5-tel), ami pl. 20 zsömle és 25 kifli esetén teljesül.


Statistics:

548 students sent a solution.
5 points:436 students.
4 points:20 students.
3 points:49 students.
2 points:32 students.
1 point:3 students.
0 point:6 students.
Unfair, not evaluated:2 solutions.

Problems in Mathematics of KöMaL, December 2006