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?
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?
Square numbers can be represented on the seven-clock (representing these numbers modulo 7). This works like the days of the week.
To maximise the profit from the crop of trees both the initial
expenditure and the long-term profit must be considered.
The Lodgepole Ping is the most expensive and the European Larch
the cheapest of the trees. Then this is offset against the profit
gained from the thinnings at both 10 and 20 years:
Sitka Spruce: -120000+10000+40000= -70000
European Larch: -158000+15000+40000= -60000
Lodgepole Pine: -130000+20000+30000= -80000
So over the first 20 years the European Larch loses the least
money. However, to discover the best tree to plant for a long term
profit over 70 years this loss must be taken from the profit gained
when the trees are felled:
SS: 1126800-70000= 1056800
EL: 1158000-60000= 1098000
LP: 1144000-80000= 1064000
So after 70 years the European Larch makes the most profit.
However after 70 years two of the trees begin to be worth less so
if the trees are to be felled at 90 years the profit must be
So after 90 years the Lodgepole Pine is the best value,
surpassing the profit gained by the European Larch after 70 years,
though not by a great deal.
So perhaps for a more long term plan it would be better to plant
a mixture of both Lodgepole Pine and European Larch, to reduce the
initial loss and to take some revenue from the Larch after 70
years, and then replant these fields with some of the profits, then
taking a larger profit at 90 years. This would give a cycle so that
some money would be collected after a shorter period of time to
sustain the plantation, as the extra £298000 gained with
the Lodgepole Pine must be compared with the twenty years extra for
I observed that in the table the possible income per hectare
after a number of years was written. I created a table with the
profit for each type of tree, taking into account the planting cost
per hectare, the profit from the thinning after 10 and 20 years
(per hectare too), and the possible income after the period of time
Now, I made a table for 70 years, with each type of tree and
with possible combinations, with the number of years left and the
The manager should plant the European Larch for 70 years,
obtaining a profit of £1098000 per hectare.
I made a similar table for 90 years:
The manager should plant the Sitka Spruce for 30 years, and then
the European Larch for 60 years.