MathDB

4

Part of 1978 Bundeswettbewerb Mathematik

Problems(2)

Bundeswettbewerb Mathematik 1978 Problem 1.4

Source: Bundeswettbewerb Mathematik 1978 Round 1

9/23/2022
In a triangle ABCABC, the points A1,B1,C1A_1, B_1, C_1 are symmetric to A,B,CA, B,C with respect to B,C,AB,C, A, respectively. Given the points A1,B1,C1A_1, B_1,C_1 reconstruct the triangle ABCABC.
Trianglesymmetryconstructionconstructive geometrygeometry
Bundeswettbewerb Mathematik 1978 Problem 2.4

Source: Bundeswettbewerb Mathematik 1978 Round 2

9/23/2022
A prime number has the property that however its decimal digits are permuted, the obtained number is also prime. Prove that this number has at most three different digits. Also prove a stronger statement.
number theoryprimedecimal representationpermutation