### Calendar Capers

Choose any three by three square of dates on a calendar page. Circle any number on the top row, put a line through the other numbers that are in the same row and column as your circled number. Repeat this for a number of your choice from the second row. You should now have just one number left on the bottom row, circle it. Find the total for the three numbers circled. Compare this total with the number in the centre of the square. What do you find? Can you explain why this happens?

### Hockey

After some matches were played, most of the information in the table containing the results of the games was accidentally deleted. What was the score in each match played?

### Clock Squares

Square numbers can be represented on the seven-clock (representing these numbers modulo 7). This works like the days of the week.

# Tree Tops

##### Stage: 3 Challenge Level:

A manager of a forestry company in Scotland has to decide which trees to plant. There are three main species to choose from, Sitka Spruce, European Larch or Lodgepole Pine.

Whatever trees are planted they have to be thinned after 10 and 20 years and the wood from the thinning is sold for a profit.

Each kind of tree has a different planting cost per hectare, a different growth rate and a different value per hectare depending on the age the tree is felled. All this information is given in the table below.

 Sitka Spruce European Larch Lodgepole Pine Planting cost per hectare (thousands of £s) 120 115 130 Profit per hectare from 10 year thin (thousands of £s) 10 15 20 Profit per hectare from 20 year thin (thousands of £s) 40 40 30

Possible income per hectare:

 After (years) (thousands of £s) (thousands of £s) (thousands of £s) 30 358 192 123 40 513 469 366 50 693 858 646 60 834 1184 950 70 1127 1158 1144 80 904 1059 1311 90 805 837 1476 100 666 783 1360

What strategy for planting and felling would you recommend to the manager in order to maximise the profit after 70 years, 90 years, more generally?