Problem K. 754. (February 2023)

K. 754. Matt and Seb are playing tic-tac-toe. When Seb wins, he will get 3 candies from Matt. When Matt wins, he will get 2 candies from Seb. (There is no draw.) After 30 games, Seb had the same number of candies as initially. How many games did Seb win?

(5 pont)

Deadline expired on March 10, 2023.

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

Megoldás. Ha Sebi nyert \(\displaystyle x\) játékot, akkor \(\displaystyle 3x\) cukrot kapott, Matyi pedig \(\displaystyle (30 - x) \cdot 2\) cukrot. Mivel Sebi cukrainak száma nem változott, így ugyanannyit adott, mint kapott, azaz \(\displaystyle 3x = 60 - 2x\), ahonnan \(\displaystyle x = 12\), azaz 12 játékot nyert Sebi, 18-at Matyi.

Statistics:

86 students sent a solution.
5 points:	70 students.
3 points:	4 students.
2 points:	1 student.
Unfair, not evaluated:	5 solutionss.
Not shown because of missing birth date or parental permission:	6 solutions.

Problems in Mathematics of KöMaL, February 2023