4
Part of 2006 Bundeswettbewerb Mathematik
Problems(2)
Cut a piece of paper
Source: Germany Bundeswettbewerb Mathematik 2006, Day 1, Problem 4
4/4/2006
A piece of paper with the shape of a square lies on the desk. It gets dissected step by step into smaller pieces: in every step, one piece is taken from the desk and cut into two pieces by a straight cut; these pieces are put back on the desk then.
Find the smallest number of cuts needed to get -gons.
digit-reduced numbers
Source: Bundeswettbewerb Mathematik 2006, round 2, problem 4
3/10/2007
A positive integer is called digit-reduced if at most nine different digits occur in its decimal representation (leading s are omitted.) Let be a finite set of digit-reduced numbers. Show that the sum of the reciprocals of the elements in is less than .
number theory unsolvednumber theory