2

Part of 1973 Bundeswettbewerb Mathematik

Problems(2)

Star shape region with centers A, B => all of [AB] centers

Source: Bundeswettbewerb Mathematik 1973, round 1, problem 2

In a planar lake, every point can be reached by a straight line from the point

A

. The same holds for the point

B

. Show that this holds for every point on the segment

[AB]

geometry proposedgeometry

Divide and append, all problem's solution

Source: Bundeswettbewerb Mathematik 1973, round 2, problem 2

We work in the decimal system and the following operations are allowed to be done with a positive integer: a) append

4

at the end of the number. b) append

0

at the end of the number. c) divide the number by

2

if it's even. Show that starting with

4

, we can reach every positive integer by a finite number of these operations

number theory proposednumber theory