MathDB

1

Part of 2001 Estonia National Olympiad

Problems(4)

37(72 + 3x) = 14**45 , find integer x

Source: 2001 Estonia National Olympiad Final Round grade 9 p1

3/12/2020
John had to solve a math problem in the class. While cleaning the blackboard, he accidentally erased a part of his problem as well: the text that remained on board was 37⋅(72+3x)=14∗∗4537 \cdot(72 + 3x) = 14**45, where ∗* marks an erased digit. Show that John can still solve his problem, knowing that xx is an integer
number theoryDigitsInteger
convex n-gon has exactly 3 obtuse interior angles

Source: 2001 Estonia National Olympiad Final Round grade 10 p1

3/12/2020
A convex nn-gon has exactly three obtuse interior angles. Find all possible values of nn.
geometryanglesconvexpolygon
angles of a convex n-gon are a,2a, ... ,na

Source: 2001 Estonia National Olympiad Final Round grade 11 p1

3/12/2020
The angles of a convex nn-gon are a,2a,...,naa,2a, ... ,na. Find all possible values of nn and the corresponding values of aa.
anglesconvexpolygongeometry
sinx = y, sin y = x. system

Source: 2001 Estonia National Olympiad Final Round grade 12 p1

3/12/2020
Solve the system of equations {sin⁡x=ysin⁡y=x\begin{cases} \sin x = y \\ \sin y = x \end{cases}
algebrasystem of equationstrigonometry