October 2006
Shapes
The diagram shows a 4 by 4 grid containing a closed path. The path always travels either horizontally or vertically and it passes through the centre of every grid-square. It goes straight through the square with the red diamond, and it turns through a right-angle at the centre of the square with the blue circle.
Draw a closed path which passes through the centre of every square in the following 8 by 8 grid. It must go straight through the squares with the red diamonds, and turn through a right-angle at the centre of each square with a blue circle.
Numbers
The diagram shows a 3 by 3 grid with a number at the end of each row and a number at the bottom of each column.
Place the numbers from 1 to 9 in the table so that each number is used once, and the numbers in each row and each column add up to the required total.
Algebra
The diagram on the right shows a number pyramid, in which the number in each box is the sum of the numbers in the two boxes on which it rests. (That is, except for the boxes at the bottom!)
Can you work out the missing number in the bottom row of the number pyramid on the left? Explain how you worked it out.
(It is not a whole number. You will need to use algebra to work it out.)
Miscellaneous
Eleven 2 by 2 squares of different colours (Brown, Dark Green, Red, Yellow, Grey, Black, Orange, Light Blue, Light Green, Dark Blue and Purple) have been placed, partly overlapping, on a 4 by 5 grid.
Clearly the Red square was placed last (since the whole of it is visible, whereas all the others are partly covered).
Can you work out the order in which all eleven squares were placed?