- January 2000, All Stages

Problems

problem Icon

How Many Days?

Stage:1 Challenge Level:Challenge Level:1

How many days are there between February 25th 2000 and March 11th?

problem Icon

Calendar Patterns

Stage:2 Challenge Level:Challenge Level:1

In this section from a calendar, put a square box around the 1st, 2nd, 8th and 9th. Add all the pairs of numbers. What do you notice about the answers?

problem Icon

How Many Times?

Stage:2 Challenge Level:Challenge Level:1

On a digital 24 hour clock, at certain times, all the digits are consecutive. How many times like this are there between midnight and 7 a.m.?

problem Icon

It Must Be 2000

Stage:2 Challenge Level:Challenge Level:2Challenge Level:2

Here are many ideas for you to investigate - all linked with the number 2000.

problem Icon

Egyptian Rope

Stage:2 Challenge Level:Challenge Level:2Challenge Level:2

The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?

problem Icon

World of Tan - Monday Morning

Stage:2 Challenge Level:Challenge Level:2Challenge Level:2

Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?

problem Icon

Watch the Clock

Stage:2 Challenge Level:Challenge Level:3Challenge Level:3Challenge Level:3

During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?

problem Icon

Calendar Cubes

Stage:2 Challenge Level:Challenge Level:3Challenge Level:3Challenge Level:3

Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.

problem Icon

Angle A

Stage:3 Challenge Level:Challenge Level:2Challenge Level:2

The three corners of a triangle are sitting on a circle. The angles are called Angle A, Angle B and Angle C. The dot in the middle of the circle shows the centre. The counter is measuring the size. . . .

problem Icon

Writ Large

Stage:3 Challenge Level:Challenge Level:2Challenge Level:2

Suppose you had to begin the never ending task of writing out the natural numbers: 1, 2, 3, 4, 5.... and so on. What would be the 1000th digit you would write down.

problem Icon

Seven Up

Stage:3 Challenge Level:Challenge Level:3Challenge Level:3Challenge Level:3

The number 27 is special because it is three times the sum of its digits 27 = 3 (2 + 7). Find some two digit numbers that are SEVEN times the sum of their digits (seven-up numbers)?

problem Icon

Times Right

Stage:3 Challenge Level:Challenge Level:3Challenge Level:3Challenge Level:3

Using the digits 1, 2, 3, 4, 5, 6, 7 and 8, mulitply a two two digit numbers are multiplied to give a four digit number, so that the expression is correct. How many different solutions can you find?

problem Icon

LOGO Challenge - Circles as Animals

Stage:3 and 4 Challenge Level:Challenge Level:2Challenge Level:2

See if you can anticipate successive 'generations' of the two animals shown here.

problem Icon

Russian Cubes

Stage:4 Challenge Level:Challenge Level:1

How many different cubes can be painted with three blue faces and three red faces? A boy (using blue) and a girl (using red) paint the faces of a cube in turn so that the six faces are painted in. . . .

problem Icon

Farhan's Poor Square

Stage:4 Challenge Level:Challenge Level:1

From the measurements and the clue given find the area of the square that is not covered by the triangle and the circle.

problem Icon

Same Arc

Stage:4 Challenge Level:Challenge Level:1

O is the centre of the circle and P, Q and R are points on the circumference. What can you say about the angles a, b, c, d, e and f ? Give reasons for your answers.

problem Icon

OK! Now Prove It

Stage:5 Challenge Level:Challenge Level:1

Make a conjecture about the sum of the squares of the odd positive integers and prove your conjecture.

problem Icon

Two Trees

Stage:5 Challenge Level:Challenge Level:1

Two trees 20 metres and 30 metres long, lean across a passageway between two vertical walls. They cross at a point 8 metres above the ground. What is the distance between the foot of the trees?

problem Icon

Ball Bearings

Stage:5 Challenge Level:Challenge Level:2Challenge Level:2

If a is the radius of the axle, b the radius of each ball-bearing, and c the radius of the hub, why does the number of ball bearings n determine the ratio c/a? Find a formula for c/a in terms of n.

problem Icon

Overarch 2

Stage:5 Challenge Level:Challenge Level:3Challenge Level:3Challenge Level:3

Bricks are 20cm long and 10cm high. How high could an arch be built without mortar on a flat horizontal surface, to overhang by 1 metre? How big an overhang is it possible to make like this?

Elsewhere...