November 2006
Shapes
The diagram shows a 7 by 7 grid containing 16 numbers.
Divide the grid into eight regions in such a way that each region contains two numbers, one of which is the region’s area and the other is the region’s perimeter. The dividing lines must follow the lines of the grid.
Try to give some explanation of how you solved the puzzle.
Numbers
The diagram below shows a sudoku puzzle with a difference. Some of the lines between adjacent cells have a number on them; this is the product of the numbers in these two cells.
The normal rules of sudoku also apply: the numbers 1 to 9 must appear once each in each row, once in each column, and once in each square block.
Can you solve this puzzle? Give some explanation of how you set about it.
Algebra
Another pyramid puzzle this month. (Look at last month’s algebra puzzle to see how a number pyramid works.)
Can you work out the two missing numbers in the bottom row of this pyramid?
Show how you worked them out.
Miscellaneous
Four people are sitting around a circular table. One is an architect, one a builder, one a carpenter, and one a doctor. Their names are Peter, Quentin, Robert, and Steve (not in that order).
Pete is sitting opposite the architect and Robert is sitting to the left of the carpenter. Steve (who is not the carpenter) is sitting opposite the doctor.
Can you identify each person’s job, and the order in which they are sitting? Explain your reasoning.