A chess king starts on one cell of a chessboard and takes a non-intersecting tour, passing through each square once, and ending up on the initial square. Show that the king has made no more than 36 diagonal moves.
SOLUTION
The king must visit the 28 perimeter squares in order; otherwise, he will create a portion of the board which is inaccessible for him. However, he can not travel from one square to a neighboring one using only diagonal moves. Therefore, he must make at least 28 horizontal/vertical moves and at most 64 – 28 = 36 diagonal moves.
Our first puzzle contest is officially over. Congratulations to the winner Kuan L.! Also, special thanks to Rajesh Kumar, Johann Sturcz, Dave Phillips, P. A. Heuser, as well as ThinkFun and Dover Books for contributing puzzles.
Time for work – 1 hour
1. Connections
Examine the diagram and find which pairs of letters are connected with each other.
Detective Roy Omoshi (upper right) is chasing a dangerous criminal (lower left) through a destroyed maze. King Kong is trying to help Roy by putting together all the pieces of the maze so that the detective can safely traverse it. Analyze the picture and find the sequence of pieces Roy Omoshi will pass through before he catches the criminal. Some pieces (#1, #7, #8) consist of multiple horizontal segments, so it is possible that the detective visits them multiple times.
Enter by the bottom red path and exit from the top of the maze. You may retrace your path, but you may not make a U-turn on a pathway. You must follow the paths in the order red, blue, yellow, and then red, blue, yellow again, changing color at the white squares.
The starting and ending positions of 7 chess pieces are shown on the board. Find the trajectories of the pieces, if you know that they do not overlap and completely cover the board. Notes: The pieces can not backtrack. Two trajectories can intersect diagonally but can not pass through the same square. Only the Knight’s has a discontinuous trajectory.
Author – Puzzle Prime
6. Sheep and Wolves
A shepherd takes his two sheep every day to a 7×7 lawn, so that they can eat the fresh grass there. However, there are five wolves on the lawn which are preying on the poor sheep. The shepherd decided to build a closed, non-intersecting fence around the sheep, so that all wolves end up on the outside. He planned the shape of the fence carefully and installed several signs showing the number of fence pieces around the corresponding cells. Can you figure out the shape of the fence the shepherd is going to build?
A square has dropped on the ground and broken into ten pieces. Accidentally, an additional, eleventh piece has fallen among the others. Can you figure out which one it is?
SOLUTION
The total number of the squares in all pieces is 70 = 8 * 8 + 6. Therefore the extra piece is the one consisted of 6 squares.
Two monks are standing on the two sides of a 2-dimensional mountain, at altitude 0. The mountain can have any number of ups and downs, but never drops under altitude 0. Prove that the monks can climb or descend the mountain at the same time on both sides, always staying at the same altitude, until they meet at the same point.
When a car is making a turn, are its front wheels parallel to each other?
SOLUTION
The front wheels are not parallel to each other. The reason is that when steering, all wheels are turning along arks that have a common center. Otherwise, the car would be drifting.
Can you draw a 3-dimensional object which looks like a square when looked from one side, a triangle when looked from a second side, and a circle when looked from a third side?
Monday, six friends went camping. Tuesday, John, Jack, and James cooked some mushrooms. Wednesday came and they ate the mushrooms. Thursday found them dead. Exactly one friend survived, how come?
SOLUTION
The six friends are called John, Jack, James, Tuesday, Wednesday, and Thursday. John, Jack, James, and Tuesday cooked the mushrooms. Wednesday joined them and they ate the mushrooms. Thursday was the one to find them dead, so he is the survivor.
In order to catch the thief, you must make your way through this Tetris maze formed by the 5 different pieces shown at the bottom. You can not climb over the blocks, just find a tunnel inside the construction.
