Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# Problem B. 4732. (October 2015)

B. 4732. The teacher of a class of 36 students enters the averages of the mathematics test grades in a $\displaystyle 6 \times 6$ table. Each student has a different mean grade. The teacher marks the largest entry in each column of the table. He finds that all of the 6 marked numbers lie in different rows. Then he marks the largest entry in each row, and finds that these all lie in different columns. Prove that the two sets of six numbers are equal.

Proposed by J. Szoldatics, Budapest

(3 pont)

Deadline expired on November 10, 2015.

### Statistics:

 197 students sent a solution. 3 points: 125 students. 2 points: 46 students. 1 point: 13 students. 0 point: 9 students. Unfair, not evaluated: 4 solutions.

Problems in Mathematics of KöMaL, October 2015