Competition #7

Q1. Who can find the best picture for the top of my blog?

Note: Pictures must be at least 2500 wide by 413 pixels wide.

I prefer something related to Titirangi or Auckland or puzzles or even Neighbourly but will consider anything you like.


Q2. Consider the presentation and functionality of my blog.

i.e. How it looks and how it works.

What do you like?

What do you not like?

What can be improved?

Note: You are not looking at the words. Pretend the words are in a foreign language that you cannot understand. Not hard for some of my puzzles, maybe?

Please be constructive.

No Drama Zone



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.


Competition #5: Magic Squares

In Competition #1 the last question has a magic square.

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

Q1. Below is a 3 x 3 magic square. Please put the numbers 1, 2, …, 9 (once only) in the cells below so that each row, column, and diagonal adds up to the same number. See the clue below if you need to!



Q2. What must each row, column, and diagonal add up to in a 4 x 4 magic square?
Read the answer below for the 3 x 3 magic square.


Q3. The solution to a 4 x 4 magic square similar to the one in Competition #1 was known at least as early as 16th century. Find an artwork that contains this magic square.

Please make sure you try the last question in Competition #1  before you answer Q3.


Read a clue to solving the 3 x 3 magic square below (scroll down):


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