2007 Cyprus MO/Lyceum/Problem 25

Problem

2007 CyMO-25.PNG

A jeweller makes crosses, according to the pattern shown above. The crosses are made from golden cyclical discs, with diameter of 1cm each. The height of a cross, which is made from 402 such discs is

$\mathrm{(A) \ } 198cm\qquad \mathrm{(B) \ } 2m\qquad \mathrm{(C) \ } 201cm\qquad \mathrm{(D) \ } 202cm\qquad \mathrm{(E) \ } 204cm$

Solution

If $n$ represents the number of the cross, then there are $4n + 2$ disks in the cross ($4n$ to count for the 4 legs of the cross, plus one for the center and one for the bottom leg). So $\displaystyle 4n+2=402 \Rightarrow n = 100$. The number of discs from top to bottom is $2n + 2 = 202 \Longrightarrow \mathrm{D}$.

See also

2007 Cyprus MO, Lyceum (Problems)
Preceded by
Problem 24
Followed by
Problem 26
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