A 1x1 square and an n-tiling is a group of n tiles placed so that every tile is contiguous along at least one side to another tile. (The tiles cannot be offset. That is, they must be placed into a grid like Scrabble tiles.) The edge length of a tiling is the total length of edges that are not touching other tiles. For instance, a 20-tiling, the edge length is 36. Required:
Prove that for all n-tilings where n >= 1, the edge length is even.

Consider the following geometry problems in 3-space enter t or f depending on whether the statement is true or false. (you must enter t or f -- true and false will not work.) f equation editorequation editor 1. a plane and a line either intersect or are parallel t equation editorequation editor 2. two planes parallel to a third plane are parallel f equation editorequation editor 3. two lines either intersect or are parallel f equation editorequation editor 4. two planes orthogonal to a third plane are parallel f equation editorequation editor 5. two planes orthogonal to a line are parallel f equation editorequation editor 6. two planes either intersect or are parallel f equation editorequation editor 7. two lines orthogonal to a third line are parallel t equation editorequation editor 8. two lines parallel to a third line are parallel t equation editorequation editor 9. two planes parallel to a line are parallel f equation editorequation editor 10. two lines parallel to a plane are parallel f equation editorequation editor 11. two lines orthogonal to a plane are parallel