# Problem C. 1305. (September 2015)

**C. 1305.** A spiral is made out of a square of side \(\displaystyle n\) units, as shown in the *figure*, by always breaking the line 1 unit before reaching the already existing part of the spiral. Similarly, a spiral is made out of a regular triangle of side \(\displaystyle 1.8n\) units by breaking the line 1.8 units before closing up. (The diagram shows the two spirals for the case of \(\displaystyle n = 4\).) For what value of n will the lengths of the two spirals be equal?

(5 pont)

**Deadline expired on October 12, 2015.**

### Statistics:

250 students sent a solution. 5 points: 102 students. 4 points: 61 students. 3 points: 10 students. 2 points: 9 students. 1 point: 5 students. 0 point: 58 students. Unfair, not evaluated: 5 solutions.

Problems in Mathematics of KöMaL, September 2015