MathDB

3

Part of 1986 Bundeswettbewerb Mathematik

Problems(2)

triangle construction given 3 points, one at each side

Source: 1986 German Federal - Bundeswettbewerb Mathematik - BWM - Round 1 p3

11/21/2022
The points SS lie on side ABAB, TT on side BCBC, and UU on side CACA of a triangle so that the following applies: AS‾:SB‾=1:2\overline{AS} : \overline{SB} = 1 : 2, BT‾:TC‾=2:3\overline{BT} : \overline{TC} = 2 : 3 and CU‾:UA‾=3:1\overline{CU} : \overline{UA} = 3 : 1. Construct the triangle ABCABC if only the points S,TS, T and UU are given.
geometryconstructionratio
non-periodic sequence

Source: Bundeswettbewerb Mathematik 1986, second stage, problem 3

5/14/2004
Let dnd_n be the last digit, distinct from 0, in the decimal expansion of n!n!. Prove that the sequence d1,d2,d3,…d_1,d_2,d_3, \ldots is not periodic.
algebra unsolvedalgebra