Problem P. 4789. (December 2015)
P. 4789. We would like to solder a so called Sierpinski-triangle from a piece of thin wire of uniform cross-section. We start from an equilateral triangle shaped frame, in which the resistance measured between the the vertices \(\displaystyle A\) and \(\displaystyle B\) is \(\displaystyle R_0\). First the wires at the midlines of the triangle are soldered to the original frame, and then the second step is to solder the wires along the midlines of three outer triangles which were created. The process is continued similarly, and a fractal like frame is created (see the figure).
What will the resistance between the points \(\displaystyle A\) and \(\displaystyle B\) be after the \(\displaystyle n\)-th step?
Deadline expired on January 11, 2016.
33 students sent a solution. 5 points: Asztalos Bogdán, Balogh Menyhért, Bekes Nándor, Blum Balázs, Csenger Géza, Di Giovanni András, Fehér 169 Szilveszter, Forrai Botond, Juhász 326 Dániel, Kasza Bence, Kovács Péter Tamás, Marozsák Tóbiás , Németh 777 Róbert, Olosz Adél, Sal Kristóf, Szentivánszki Soma , Szick Dániel, Tibay Álmos, Tófalusi Ádám, Tomcsányi Gergely, Tóth Adrián, Török Péter, Varga-Umbrich Eszter, Veres Károly, Weisz Pál, Wiandt Péter. 3 points: 2 students. 1 point: 3 students. 0 point: 2 students.