4
Part of 1971 Bundeswettbewerb Mathematik
Problems(2)
Funny movement, but no tour possible
Source:
6/14/2006
Let and be two horizontal neighbouring squares on a chess board, on the left and on the right. On the left square there is a stone that shall be moved around the board. The following moves are allowed:
1) move it one square upwards
2) move it one square to the right
3) move it one square down and one square to the left (diagonal movement)
Example: you can get from to , and .
Show that for no there is tour visting every square exactly once and ending in .
quadraticsmodular arithmetic
Parallel intersecting broken line 501 times
Source: Bundeswettbewerb Mathematik 1971, round 2 problem 4
6/14/2006
Inside a square with side lengths a broken line of length without selfintersection is drawn.
Show that there is a line parallel to a side of the square that intersects the broken line in at least points.
probabilityinequalitiesexpected valuetriangle inequalitycombinatorics proposedcombinatorics