Special numbers - I'm thinking of a two-digit number that is rather special because when you add the sum of its digits to the product of its digits you get the original number.  Can you work out my number?

For example, let's try 25  The sum of its digits is 2+5=7.  The product of its digits is 2x5=10. When we add the sum and the product of the digits we get 7+10=17, which is not our original number of 25, so 25 can't be the special number.  Can you find it, if so is there more than one special number - can you find them?

Greatest Product - choose a number then find integers that when added together produce your number, e.g. choose 15, then 15 = 2+3+4+6.  Now find the product of these integers, i.e. 2x3x4x6=144.  Can you find a larger product of integers that add up to 15? Once you think you have the greatest product, try this again with other numbers.  Can you spot a pattern?

Let's bake some pies - Imagine we have a rectangular sheet of pastry that is 60cm by 30cm.  Each pie needs two pastry circles, one 10cm diameter, the other 6cm diameter. We can use the leftover pastry to roll a smaller rectangle, but we can only use the leftover pastry in this way once.  What is the largest number of fruit pies we can make?

Digging for gold - In the 19th century, many adventurers travelled to North America to search for gold. Dan Jackson owned some land where gold had been found. Instead of digging for the gold himself, he rented plots of land to the adventurers.