Sudoku is a great skill based puzzle originating from Japan. Sudoku is a Japanese word, which means “single digit” or “single number”. The game is based on a square divided into n rows and columns. The common version of the game uses 9 rows and columns. Let us look at examples where the square is either 4 x 4 or 6 x 6. The rules of the game are actually very easy. For the 4 x 4 game, the numbers 1 to 4 must be filled in each row, column and smaller 2 x 2 boxes. Each number in a row, column or box must be used exactly once! A 4 x 4 Sudoku puzzle looks as follows.

The following example shows how to work through the above puzzle to get a solution. The main idea is to consider all the valid possible solutions and then eliminate the options that do not satisfy the rules of the game.

Complete the following Sudoku puzzles:

Note that for the 6 x 6 game, we need to fill in the numbers 1 to 6. The smaller boxes are now of size 2 x 3, i.e., two rows and 3 columns.

Ali has bought a chocolate gift box for his friend. He wants to wrap it using a wrapping paper. He does not have a large sheet of wrapping paper, but rather his sheet looks like image below. By folding the paper along the lines, he can still make a perfect cube to wrap the box completely.

Such a wrapping paper is called a “net” of a cube. Note how there are six sides of the box and the wrapping paper is also divided into six blocks. There are also exist additional “nets” for a box. One easy way to find a net is to think of a cube as four sides, a top and a bottom. Arrange four squares in a line. These are the sides. Now put the top square on one side of this line, and the bottom on the other. It does not matter where on each side, they all work. How many such nets can you find? There are other layouts which work, but you need to think about them a bit more. In total, there are eleven different nets for a cube. Can you find them all in the Figure on the next page? Find all the nets for a cube in the following image.

Which cube can be obtained by folding the given net?

Which cube can be obtained by folding the given net?


This puzzle dates back to the beginning of the 20th century. You have four shapes colored blue, red, green and yellow. The goal is to combine these four pieces into the capital English alphabet “T”. You are allowed to rotate the pieces as you wish and even turn them over, but they must not overlap each other in the final letter. Open the Word file “Shapes” on your lab computers, where you can play around with these shapes on the computer by moving them around. You may find the options to rotate and flip the images useful in working out a solution. Locate these options in the menu after you select an image.

There is at least one more extra symmetric shape that can be formed from this set. An “isosceles trapezoid” is a four-sided figure in which two opposite lines are parallel and the other two sides are of equal length but not parallel. Can you form an isosceles trapezoid using these pieces?

How many other interesting shapes can you make using these pieces?