Indices

problem
Power crazy

Age

11 to 14

Challenge level

What can you say about the values of n that make $7^n + 3^n$ a multiple of 10? Are there other pairs of integers between 1 and 10 which have similar properties?
problem
Powerful zeros

Age

14 to 16

Challenge level

How many zeros are there at the end of $3^4 \times 4^5 \times 5^6$?
problem
Largest expression

Age

14 to 16

Challenge level

Which of these five algebraic expressions is largest, given $x$ is between 0 and 1?
problem
Maundy money

Age

11 to 14

Challenge level

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

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

Age

14 to 16

Challenge level

Is it true that $99^n$ has 2n digits and $999^n$ has 3n digits? Investigate!
problem
Really Mr. Bond

Age

14 to 16

Challenge level

115^2 = (110 x 120) + 25, that is 13225 895^2 = (890 x 900) + 25, that is 801025 Can you explain what is happening and generalise?
problem
Lastly - well

Age

11 to 14

Challenge level

What are the last two digits of 2^(2^2003)?
problem
The public key

Age

16 to 18

Challenge level

Find 180 to the power 59 (mod 391) to crack the code. To find the secret number with a calculator we work with small numbers like 59 and 391 but very big numbers are used in the real world for this.
problem
Perfectly square

Age

14 to 16

Challenge level

The sums of the squares of three related numbers is also a perfect square - can you explain why?