Mathematical and Physical Journal
for High Schools
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Problem C. 965. (December 2008)

C. 965. The pattern in the Figures consists of black, white and grey squares. Which Figure in the sequence will contain 2112 grey squares?

(5 pont)

Deadline expired on January 15, 2009.

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

Megoldás. Az n-edik ábrán (2n-1)2 négyzet van. Ebből n2 fekete és (n-1)2 fehér. Vagyis a szürkék száma: (2n-1)2-n2-(n-1)2=2n2-2n=2n(n-1)=2112. Innen n=33, vagyis a 33. ábrán van 2112 darab szürke négyzet.


387 students sent a solution.
5 points:167 students.
4 points:129 students.
3 points:39 students.
2 points:17 students.
1 point:5 students.
0 point:7 students.
Unfair, not evaluated:23 solutionss.

Problems in Mathematics of KöMaL, December 2008