### There are 16 results

Broad Topics >

Numbers and the Number System > Common factors

##### Age 14 to 16 Challenge Level:

Find the largest integer which divides every member of the
following sequence: 1^5-1, 2^5-2, 3^5-3, ... n^5-n.

##### Age 14 to 16 Challenge Level:

Take any pair of two digit numbers x=ab and y=cd where, without
loss of generality, ab > cd . Form two 4 digit numbers r=abcd
and s=cdab and calculate: {r^2 - s^2} /{x^2 - y^2}.

##### Age 14 to 16 Challenge Level:

Data is sent in chunks of two different sizes - a yellow chunk has
5 characters and a blue chunk has 9 characters. A data slot of size
31 cannot be exactly filled with a combination of yellow and. . . .

##### Age 14 to 16 Challenge Level:

Make a line of green and a line of yellow rods so that the lines
differ in length by one (a white rod)

##### Age 14 to 16 Challenge Level:

The triangle OMN has vertices on the axes with whole number co-ordinates. How many points with whole number coordinates are there on the hypotenuse MN?

##### Age 11 to 14 Challenge Level:

Follow this recipe for sieving numbers and see what interesting patterns emerge.

##### Age 11 to 14 Challenge Level:

Can you find a relationship between the number of dots on the
circle and the number of steps that will ensure that all points are
hit?

##### Age 7 to 14 Challenge Level:

Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?

##### Age 11 to 14 Challenge Level:

How many integers between 1 and 1200 are NOT multiples of any of
the numbers 2, 3 or 5?

##### Age 11 to 14 Challenge Level:

A and B are two interlocking cogwheels having p teeth and q teeth respectively. One tooth on B is painted red. Find the values of p and q for which the red tooth on B contacts every gap on the. . . .

##### Age 11 to 14 Challenge Level:

I put eggs into a basket in groups of 7 and noticed that I could
easily have divided them into piles of 2, 3, 4, 5 or 6 and always
have one left over. How many eggs were in the basket?

##### Age 11 to 14 Challenge Level:

What is the smallest number of answers you need to reveal in order
to work out the missing headers?

##### Age 14 to 16 Challenge Level:

Take any pair of numbers, say 9 and 14. Take the larger number,
fourteen, and count up in 14s. Then divide each of those values by
the 9, and look at the remainders.

##### Age 11 to 14 Challenge Level:

Given the products of adjacent cells, can you complete this Sudoku?

##### Age 14 to 16 Challenge Level:

##### Age 11 to 14 Challenge Level:

Here is a chance to create some Celtic knots and explore the mathematics behind them.