Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# Problem C. 1349. (March 2016)

C. 1349. Charlie and his friends like playing poker dice. Charlie decided to play a prank on his friends, and on one of the five dice he eliminated the central dots of the faces with 3 and 5 dots. Now that die shows one 1, two 2's, two 4's and one 6. The next time they played, no one noticed the trick.

If one rolls the five dice prepared in this way, what is the probability that at least four identical numbers will appear on top?

(5 pont)

Deadline expired on April 11, 2016.

### Statistics:

 30 students sent a solution. 5 points: Csapó Márton, Csorba Benjámin, Fülöp Ágota, Horváth András János, Kasó Ferenc, Kiss Vivien Mercédesz, Kormányos Hanna Rebeka, Kósa Szilárd, Lévay Mátyás, Matusek Márton, Nagy 911 Viktória, Sudár Ákos, Szabó Alexandra, Szajkó Gréta, Szauer Marcell, Török Réka . 4 points: Dankowsky Anna Zóra, Kocsis Júlia. 2 points: 2 students. 1 point: 2 students. 0 point: 8 students.

Problems in Mathematics of KöMaL, March 2016