Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# Problem K. 263. (October 2010)

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 pont)

Deadline expired on November 10, 2010.

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

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:

 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