February 2006
Shapes
The diagram shows a square of side 10 cm that has an isosceles right-angled triangle stuck on the side. The maximum width of the shape is 15 cm. Show how to cut the shape into three pieces which can be arranged to form a square.
(Hint: Work out the area of the shape. This will tell you how long the sides of the square need to be.)
Numbers
Here is a ‘product sudoku’. It has to be filled with the digits 1–9 so that
- Each row contains the digits 1–9.
- Each column contains the digits 1–9.
- The product of the digits in each region marked with a dotted line is equal to the number in the top left-hand corner of the region.
(In case you are familiar with normal sudoku, note that there are no 3 by 3 squares on this grid. That rule does not apply.)
Solve the puzzle and give some indication of how you did it.
Algebra
I am thinking of a three-digit number with three different digits. I form all the possible three-digit numbers that I can with the three digits of my number, not including my original number. (There are five of them.) I add up my five rearrangements and find that the total is 3961. What was my original number?
(Hint: Use the same type of method as for the January 2006 Algebra puzzle.)
Miscellaneous
Hannah, Isobel, Jane, Kim, and Lucy had a pizza dinner at a restaurant. Each of them had three of the following five toppings: sausage, pepperoni, mushroom, olives, and green pepper. The only topping that Jane and Lucy had in common was sausage. The only topping that Hannah and Isobel had in common was pepperoni. The only topping that Lucy and Kim had in common was mushroom. The only topping that Hannah and Kim had in common was green pepper. Identify the toppings that each of them had on their pizza.