Problem K. 739. (November 2022)

K. 739. Phil made the following observations throughout a certain period in autumn:

1. During that period, there were 11 days when it rained.

2. A rainy morning was always followed by a sunny afternoon.

3. Altogether, there were 9 sunny mornings and 12 sunny afternoons.

How many days were there when it did not rain at all?

(5 pont)

Deadline expired on December 12, 2022.

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

Megoldás. Jelölje \(\displaystyle A\) a napos-napos, \(\displaystyle B\) a napos-esős, \(\displaystyle C\) az esős-esős és \(\displaystyle D\) az esős-napos napok számát. Az 1. állítás alapján \(\displaystyle B + C + D = 11\). A 2. állítás miatt \(\displaystyle C = 0\), a 3. állítás miatt \(\displaystyle A + B = 9\) és \(\displaystyle A + D = 12\). Azaz \(\displaystyle 2A + B + D = 21\), valamint \(\displaystyle B + D = 11\), amiből \(\displaystyle 2A = 10\), \(\displaystyle A = 5\). Tehát 5 napon nem esett egyáltalán az eső.

Statistics:

105 students sent a solution.
5 points:	55 students.
4 points:	8 students.
3 points:	4 students.
2 points:	4 students.
1 point:	2 students.
0 point:	11 students.
Unfair, not evaluated:	12 solutionss.
Not shown because of missing birth date or parental permission:	9 solutions.

Problems in Mathematics of KöMaL, November 2022