Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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Problem C. 867. (October 2006)

C. 867. Starting from the origin in the usual Cartesian coordinate system, a broken line segment is drawn. We arrive back at the y-axis in every fourth step, see the figure.

Using a certain ball-pen and a coordinate system with unit length of 0.5 cm, we draw broken line segments of length 8000 meters as in the figure. Count how many times we arrive back at the y-axis.

(5 pont)

Deadline expired on November 15, 2006.

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





Másodfokú egyenlőtlenség megoldása nélkül is kitalálható, hogy melyik a legnagyobb n egész szám, amire teljesül: n=601.


459 students sent a solution.
5 points:235 students.
4 points:21 students.
3 points:19 students.
2 points:27 students.
1 point:72 students.
0 point:66 students.
Unfair, not evaluated:19 solutions.

Problems in Mathematics of KöMaL, October 2006