Mathematical and Physical Journal
for High Schools
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Problem B. 4525. (March 2013)

B. 4525. Given n points in the interior of a regular triangle \mathcal{T}, prove that \mathcal{T} can be covered with 2n+1 regular triangles whose sides are parallel to the sides of \mathcal{T} such that they contain none of the n points in their interior. Also prove that the covering is not necessarily possible with 2n triangles.

Suggested by D. Pálvölgyi, Budapest

(6 pont)

Deadline expired on April 10, 2013.

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

Megoldási ötlet: Teljes indukció a pontok számával.


18 students sent a solution.
6 points:Havasi 0 Márton, Janzer Olivér, Maga Balázs, Tossenberger Tamás, Williams Kada.
5 points:Badacsonyi István András, Baran Zsuzsanna, Csépai András, Nagy Róbert, Petrényi Márk, Venczel Tünde.
4 points:2 students.
2 points:1 student.
1 point:4 students.

Problems in Mathematics of KöMaL, March 2013