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Can you use the clues to complete these 5 by 5 Mathematical Sudokus?
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
A game in which players take it in turns to choose a number. Can you block your opponent?
Given the products of diagonally opposite cells - can you complete this Sudoku?
The clues for this Sudoku are the product of the numbers in adjacent squares.
An environment which simulates working with Cuisenaire rods.
Ben, Jack and Emma passed counters to each other and ended with the same number of counters. How many did they start with?
Caroline and James pick sets of five numbers. Charlie tries to find three that add together to make a multiple of three. Can they stop him?
Lyndon chose this as one of his favourite problems. It is accessible but needs some careful analysis of what is included and what is not. A systematic approach is really helpful.
Take a complicated fraction with the product of five quartics top and bottom and reduce this to a whole number. This is a numerical example involving some clever algebra.
This article explains various divisibility rules and why they work. An article to read with pencil and paper handy.
The items in the shopping basket add and multiply to give the same amount. What could their prices be?
Can you produce convincing arguments that a selection of statements about numbers are true?
Take any prime number greater than 3 , square it and subtract one. Working on the building blocks will help you to explain what is special about your results.
Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors?
Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?
What is the largest number which, when divided into 1905, 2587, 3951, 7020 and 8725 in turn, leaves the same remainder each time?
Three people chose this as a favourite problem. It is the sort of problem that needs thinking time - but once the connection is made it gives access to many similar ideas.
Can you create a Latin Square from multiples of a six digit number?
Find the largest integer which divides every member of the following sequence: 1^5-1, 2^5-2, 3^5-3, ... n^5-n.
Find the smallest numbers a, b, and c such that: a^2 = 2b^3 = 3c^5 What can you say about other solutions to this problem?
Can you make lines of Cuisenaire rods that differ by 1?
Each letter represents a different positive digit AHHAAH / JOKE = HA What are the values of each of the letters?
When if ever do you get the right answer if you add two fractions by adding the numerators and adding the denominators?
An introduction to coding and decoding messages and the maths behind how to secretly share information.
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.
A polite number can be written as the sum of two or more consecutive positive integers, for example 8+9+10=27 is a polite number. Can you find some more polite, and impolite, numbers?
Given any 3 digit number you can use the given digits and name another number which is divisible by 37 (e.g. given 628 you say 628371 is divisible by 37 because you know that 6+3 = 2+7 = 8+1 = 9). The question asks you to explain the trick.
Explore the factors of the numbers which are written as 10101 in different number bases. Prove that the numbers 10201, 11011 and 10101 are composite in any base.
Use the fact that: x²-y² = (x-y)(x+y) and x³+y³ = (x+y) (x²-xy+y²) to find the highest power of 2 and the highest power of 3 which divide 5^{36}-1.
Find and explain a short and neat proof that 5^(2n+1) + 11^(2n+1) + 17^(2n+1) is divisible by 33 for every non negative integer n.
An account of methods for finding whether or not a number can be written as the sum of two or more squares or as the sum of two or more cubes.
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?
In how many ways can the number 1 000 000 be expressed as the product of three positive integers?
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?
How many zeros are there at the end of the number which is the product of first hundred positive integers?
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?
Consider numbers of the form un = 1! + 2! + 3! +...+n!. How many such numbers are perfect squares?
The nth term of a sequence is given by the formula n^3 + 11n. Find the first four terms of the sequence given by this formula and the first term of the sequence which is bigger than one million. Prove that all terms of the sequence are divisible by 6.
Find the smallest positive integer N such that N/2 is a perfect cube, N/3 is a perfect fifth power and N/5 is a perfect seventh power.
Prove that if a^2+b^2 is a multiple of 3 then both a and b are multiples of 3.
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}.
How many noughts are at the end of these giant numbers?
The sum of the cubes of two numbers is 7163. What are these numbers?
In turn 4 people throw away three nuts from a pile and hide a quarter of the remainder finally leaving a multiple of 4 nuts. How many nuts were at the start?