Problem C. 945. (May 2008)

C. 945. On 1 March, 2008, the Hungarian National Bank withdrew 1 and 2-forint (HUF) coins from circulation. At the cash desk, prices of individual items are not rounded, but the total is rounded to the nearest five. An information leaflet formulates the rule of rounding as follows: Totals ending in 1 or 2 are rounded down to 0; totals ending in 3 or 4 are rounded up to 5; totals ending in 6 or 7 are rounded down to 5; totals ending in 8 or 9 are rounded up to 0. Martin buys two croissants in the little shop on the corner every morning. In a few days, he saves exactly the price of a croissant. Given that a croissant costs more than 10 forints, what may be the price of a croissant so that he can save that amount in the shortest possible time?

(5 pont)

Deadline expired on June 16, 2008.

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

Megoldás: Két kifli ára páros szám. A 0, 2, 4, 6, 8 végződések esetén a megtakarítás rendre: 0, 2, -1, 1, -2. Mivel a megtakarítás a leggyorsabban következik be, ezért két kifli ára 2-re végződik (így Marci mindennap 2 Ft-ot takarít meg), azaz egy kifli ára vagy 1-re, vagy 6-ra végződik. A megtakarítás páros szám, ezért a kifli ára is páros szám: vagyis 16 Ft.

Statistics:

137 students sent a solution.
5 points:	109 students.
4 points:	14 students.
3 points:	10 students.
2 points:	3 students.
0 point:	1 student.

Problems in Mathematics of KöMaL, May 2008