Powers and roots

problem

Largest Number

Age

11 to 14

Challenge level

1 out of 3

What is the largest number you can make using the three digits 2, 3 and 4 in any way you like, using any operations you like? You can only use each digit once.
problem

Sept 03

Age

11 to 14

Challenge level

2 out of 3

What is the last digit of the number 1 / 5^903 ?
problem

Maundy Money

Age

11 to 14

Challenge level

2 out of 3

How much money did the Queen give away in pence as a power of 2?
problem

Age of Augustus

Age

11 to 14

Challenge level

2 out of 3

The English mathematician Augustus de Morgan has given his age in algebraic terms. Can you work out when he was born?
problem

What an Odd Fact(or)

Age

11 to 14

Challenge level

3 out of 3

Can you show that 1^99 + 2^99 + 3^99 + 4^99 + 5^99 is divisible by 5?
problem

eNRICHing Experience

Age

14 to 16

Challenge level

1 out of 3

Find the five distinct digits N, R, I, C and H in the following nomogram
problem

Powers of Four

Age

14 to 16

Challenge level

1 out of 3

Can you work out the value of x in this 'power-full' equation?
problem

Twelve Cubed

Age

14 to 16

Challenge level

1 out of 3

A wooden cube with edges of length 12cm is cut into cubes with edges of length 1cm. What is the total length of the all the edges of these centimetre cubes?
problem

Rationals Between...

Age

14 to 16

Challenge level

2 out of 3

What fractions can you find between the square roots of 65 and 67?
problem

Consecutive Squares

Age

14 to 16

Challenge level

2 out of 3

The squares of any 8 consecutive numbers can be arranged into two sets of four numbers with the same sum. True of false?