MathDB

2

Part of 2022 Vietnam National Olympiad

Problems(2)

VMO 2022 problem 2 day 1

Source: Vietnam Mathematical Olympiad 2022 problem 2 day 1

3/4/2022
Find all function f:R+→R+f:\mathbb R^+ \rightarrow \mathbb R^+ such that: f\left(\frac{f(x)}{x}+y\right)=1+f(y),   \forall x,y \in \mathbb R^+.
vmoalgebrafunctional equationfunction
VMO 2022 problem 6 day 2

Source: Vietnam Mathematical Olympiad problem 6 day 2

3/5/2022
We are given 4 similar dices. Denote xi(1≤xi≤6)x_i (1\le x_i \le 6) be the number of dots on a face appearing on the ii-th dice 1≤i≤41\le i \le 4 a) Find the numbers of (x1,x2,x3,x4)(x_1,x_2,x_3,x_4) b) Find the probability that there is a number xjx_j such that xjx_j is equal to the sum of the other 3 numbers c) Find the probability that we can divide x1,x2,x3,x4x_1,x_2,x_3,x_4 into 2 groups has the same sum
vmocombinatoricsprobability