Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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Problem B. 4783. (March 2016)

B. 4783. A flea is jumping on the vertices of a square \(\displaystyle ABCD\). It starts at vertex \(\displaystyle A\), and in each jump he moves to an adjacent vertex with a probability of \(\displaystyle \frac{1}{2}\) for each. The flea will stop when it has reached all vertices at least once. For each vertex, determine the probability of its being the last vertex.

(5 pont)

Deadline expired on April 11, 2016.


109 students sent a solution.
5 points:52 students.
4 points:34 students.
3 points:12 students.
2 points:3 students.
1 point:2 students.
0 point:5 students.
Unfair, not evaluated:1 solution.

Problems in Mathematics of KöMaL, March 2016