Problem 1.1 Paths
A unit cube is a cube whose edges are each one unit long.
Two vertices of a unit cube are labelled X and Y so that
they are diametrically opposite each other.
How many paths of length 3 units are there from X to Y
that follow the edges of the cube? |
 |
Problem 1.2 Number of Smaller Cubes
A white cube whose sides are n units long is painted
yellow. It is then sliced into n3 smaller cubes of
equal size. Find a general formula for the number of smaller cubes
that have exactly one yellow side. |
Problem 1.3 The Date
What is the date when the month of February 2002 is 21 660 minutes old? |
Problem 1.4 How Much?
I want to buy 50 nails. I can buy a package of 24 nails for 75
cents, or I can buy the nails individually for 5 cents each. How
much can I save if I buy three packages of nails instead of buying the
nails individually? |
Problem 1.5 How Long?
How long is the night when the sun sets at 6:24 PM and rises at 7:13
AM? |
Problem 1.6 Storm Clouds
It takes 12 seconds for storm clouds to travel 3 km. How long
does it take the storm clouds to travel 0.20 km? |
|
Problem 1.7 A Bus
A bus runs between two cities 1200 kilometres apart at an average speed
of 60 km/h. How much would the bus's speed have to increase in order
to decrease the running time by 2 hours? |
|
Problem 1.8 A Train
A train 0.4 km long travelling at a speed of 80 km/h enters a tunnel
0.6 km long. How many seconds will it take the train to pass the
tunnel completely? |
