Competition #6: Moving counters

Please read the rules in Competition #1 or in the New Competition  (#2) before you answer the questions below.

Q1. In the board below place two coins (or counters) on the black circles and two different coins of counters on the white squares.

The object is to change around the coins on the black and white circles by moving to any point of the star. You may keep moving any counter any distance (along the lines) in one turn until you are blocked by a coin.

Question: What is the minimum number of moves to solve this?

 

Q2. In the board below place four coins or counters of one colour (say black!) on the black circles and 4 different ones (say white) on the big white circles. The central square is empty. Alternatively heads and tails will do if using coins.

The object is to get the coins/counters to change places.

The counters only go in the obvious direction of travel.

A move consists of moving one step forward to an empty square or jumping over one opposite “coloured” counter to an empty square. You do not have to use alternate colours on you moves. i.e. you can use the same colour more than once in consecutive moves.

Solve the puzzle. How may moves?

 

Q3. Think about the solution to this puzzle before you try it!

I have two coins (heads facing up) touching each other vertically.

I roll the top coin half-way around the bottom (fixed) coin (i.e. until it is now at the bottom). Will the “head” now be facing up or down?

 

Q4. Arrange eight queens on a chess board so that no queen can attack any other queen.

Try to find two solutions that are not rotations or reflections.

 

Q5. Take six coins and arrange them in a triangle. Your goal is to rearrange the coins into a hexagon in four moves. Each move consists of sliding a single coin to a new location. The new location must be touching at least two other coins at each step.