Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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Problem K. 225. (November 2009)

K. 225. Little Pete is playing with six identical square sheets of plastic on the table. He lays a square on the table, then he lays the next one, always making sure that the newly laid square joins at least one of the previous ones along the full length of an edge. (Vertices always meet vertices.) Show that the perimeters of all those figures obtained that may form the net of a cube unfolded in the plane, is the same.

(6 pont)

Deadline expired on December 10, 2009.

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

Megoldás. Induljunk ki egy négyzetből. Ennek kerülete legyen 4 egységnyi. A második letett négyzet ehhez teljes oldallal csatlakozik, tehát a kapott alakzat kerülete az előzőéhez képest 1-gyel csökken, majd 3-mal nő, azaz összesen 2-vel nő, így értéke 6 lesz.

Statistics:

 170 students sent a solution. 6 points: 94 students. 5 points: 10 students. 4 points: 13 students. 3 points: 24 students. 2 points: 17 students. 1 point: 5 students. 0 point: 3 students. Unfair, not evaluated: 4 solutions.

Problems in Mathematics of KöMaL, November 2009