"Interesting" math problems Since I have naught to do right now and the weather is not great whatsoever, I'm going through a Math problem book I found covered in dust sitting on the shelf at my folks' - it's from 1960 entitled (if word for word translation) "Mathematical Sharpness" by B. Kordemsky originally in Russian, but I do my best to translate for yous ^^ Interesting doesn't necessarely mean difficult, but I looked ahead a bit and this book will end up in complete fireworks in terms of difficulty. Contains 369 different puzzles and I will be working my way through this book for the days/weeks to come and will post, after I've solved something, the ones I like/had trouble with or both, who knows. I'll number the puzzles the way they are given in the book, perhaps someone recognizes the book and the puzzles :) 6) http://www.upload.ee/image/3584987/Puzzle6.jpg [Broken] A gardener, represented as * is attending to his apple trees, which are represented by the dots. The gardener cannot move diagonally, may not enter the red squares and may not walk on already treaded path. Show a way for the gardener to attend to Every tree and end up where he started. I like this one since I used to be a hardcore nokia 3310 snake player and I kind of saw the path almost instantly, made me smile :) 8) Here's one that reads so funny to me and if you're a visual thinker, it might make you go haywire at first: How many cats are in a quadrangular room if in every corner of the room there's a cat, every cat in the room is facing 3 cats and there's a cat sitting on every cat's tail. 9) This one is tricky, so simple, but yet so difficult to see :D There are two pencils red and green held together so that their bottom parts are in the same position ( you hold two pencils together and set them on a horizontal plane to "even" them out). The red pencil's bottom part is covered in paint along 1 cm. While holding the pencils still tightly together, you begin to move the red pencil 1 cm down and then 1 cm back up, down 1 cm, up 1 cm - the green pencil stays fixed. You complete the up-down cycle 10 times hence you make 20 moves total. Once finished, what is the length of the stain of paint that is covering the red pencil if the paint does not dry or fade?