Order KöMaL! Competitions Portal

K. 263. Charles writes the numbers 3, 5, 6 on three cards, and Charlotte writes the numbers 8, 9, 10 on three cards. Each of them selects two cards at random out of the three of their own. Charles multiplies his two numbers, and Charlotte adds hers. What is the probability that Charles will get a greater number than Charlotte?

(6 points)

This problem is for grade 9 students only.

Deadline expired on 10 November 2010.

Google Translation (Sorry, the solution is published in Hungarian only.)

Megoldás. Karcsi szorzatai 15, 18, 30 lehet, Karola összegei pedig 17, 18, 19. Összesen $\displaystyle 3\cdot 3=9$ féle képpen hasonlíthatják össze eredményeiket, ezek közül pedig akkor lesz Karcsié a nagyobb, ha $\displaystyle 3\cdot 6>8+9$, illetve $\displaystyle 5\cdot 6$ mindig nagyobb, mint Karola összegei, tehát 4 esetben. Ezért annak a valószínűsége, hogy Karcsi eredménye nagyobb Karoláénál $\displaystyle \frac49$.

Statistics on problem K. 263.
 353 students sent a solution. 6 points: 234 students. 5 points: 40 students. 4 points: 31 students. 3 points: 10 students. 2 points: 6 students. 1 point: 12 students. 0 point: 3 students. Unfair, not evaluated: 17 solutions.

• Problems in Mathematics of KöMaL, October 2010

•  Our web pages are supported by: ELTE Morgan Stanley