# 2020-20 Efficient triangulation of surfaces

Let $$S_g$$ denote the closed orientable connected surface of genus $$g$$. Suppose we glue triangles along the edges so that the resulting space is $$S_g$$ and the intersection of any two triangles are either empty or a single edge. Let $$n(g)$$ be the minimum number of triangles one needs to make $$S_g$$ while satisfying the above rule. What are $$n(1), n(2), n(3)$$? Does the limit $$\lim_{g \to \infty} n(g)/g$$ exist?

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# Solution: 2020-19 Continuous functions

Let $$n$$ be a positive integer. Determine all continuous functions $$f: [0, 1] \to \mathbb{R}$$ such that
$f(x_1) + \dots + f(x_n) =1$
for all $$x_1, \dots, x_n \in [0, 1]$$ satisfying $$x_1 + \dots + x_n = 1$$.

The best solution was submitted by 김유일 (2020학번) Congratulations!

Here is his solution of problem 2020-19.

Other solutions was submitted by 길현준 (수리과학과 2018학번, +3), 채지석 (수리과학과 2016학번, +3), 이준호 (수리과학과 2016학번, +2).

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