MathDB

7

Part of 1994 IMO Shortlist

Problems(2)

A set of 2^n-1 points

Source: IMO Shortlist 1994, C7

10/22/2005
Let n>2 n > 2. Show that there is a set of 2nāˆ’1 2^{n-1} points in the plane, no three collinear such that no 2n 2n form a convex 2n 2n-gon.
combinatoricsIMO Shortlistcombinatorial geometryconvex polygonpolygon
A wobbly number

Source: IMO Shortlist 1994, N7

10/22/2005
A wobbly number is a positive integer whose digits are alternately zero and non-zero with the last digit non-zero (for example, 201). Find all positive integers which do not divide any wobbly number.
number theorydecimal representationIMO ShortlistDivisibility