article
An introduction to number theory
An introduction to some beautiful results in Number Theory.
Number theory
problem
Always Perfect
Age
14 to 18
Challenge level
Show that if you add 1 to the product of four consecutive numbers the answer is ALWAYS a perfect square.
problem
Impossibilities
Age
11 to 14
Challenge level
Just because a problem is impossible doesn't mean it's difficult...
problem
Overlaps
Age
11 to 14
Challenge level
Can you find ways to put numbers in the overlaps so the rings have equal totals?
article
Binomial Coefficients
An introduction to the binomial coefficient, and exploration of some of the formulae it satisfies.
problem
Filling the gaps
Age
14 to 16
Challenge level
Which numbers can we write as a sum of square numbers?
problem
A little light thinking
Age
14 to 16
Challenge level
Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?
problem
How much can we spend?
Age
11 to 14
Challenge level
A country has decided to have just two different coins, 3z and 5z
coins. Which totals can be made? Is there a largest total that
cannot be made? How do you know?
problem
Data Chunks
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 blue
chunks, explore what sizes near to 31 can, or cannot, be exactly
filled.
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.