Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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Problem K. 379. (September 2013)

K. 379. Kate sewed a button on her coat. The button has four holes in it as shown in the figure (the holes form the four vertices of a square). As the thread is pulled through the holes again and again, it produces various patterns, as viewed from the front. One such pattern is shown in the figure. How many different patterns may result, provided that at least two holes need to be used to fix the button to the coat?

(6 pont)

Deadline expired on October 10, 2013.

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

Megoldás. Bármelyik két lyuk vagy össze van kötve cérnával, vagy nem. Ez minden lyuk-párra nézve 2 lehetőség. Mivel összesen $\displaystyle \binom42=6$ lehetséges lyuk-páros van, ez $\displaystyle 2^6=64$ lehetőség lenne, azonban ebből ki kell vonni azt az egy esetet, amikor semelyik két lyuk nincs összekötve.

Tehát 63 mintát láthatunk a varrás után.

Statistics:

 247 students sent a solution. 6 points: 125 students. 5 points: 8 students. 4 points: 11 students. 3 points: 5 students. 2 points: 9 students. 1 point: 42 students. 0 point: 41 students. Unfair, not evaluated: 6 solutions.

Problems in Mathematics of KöMaL, September 2013