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Find the exact values of x, y and a satisfying the following system of equations: 1/(a+1) = a - 1 x + y = 2a x = ay

Challenge Level

Solve the system of equations to find the values of x, y and z: xy/(x+y)=1/2, yz/(y+z)=1/3, zx/(z+x)=1/7

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Five children went into the sweet shop after school. There were choco bars, chews, mini eggs and lollypops, all costing under 50p. Suggest a way in which Nathan could spend all his money.

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Can you make a tetrahedron whose faces all have the same perimeter?

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A group of 20 people pay a total of £20 to see an exhibition. The admission price is £3 for men, £2 for women and 50p for children. How many men, women and children are there in the group?

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To make 11 kilograms of this blend of coffee costs £15 per kilogram. The blend uses more Brazilian, Kenyan and Mocha coffee... How many kilograms of each type of coffee are used?

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If: A + C = A; F x D = F; B - G = G; A + H = E; B / H = G; E - G = F and A-H represent the numbers from 0 to 7 Find the values of A, B, C, D, E, F and H.

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When asked how old she was, the teacher replied: My age in years is not prime but odd and when reversed and added to my age you have a perfect square...

Challenge Level

Add up all 5 equations given below. What do you notice? Solve the system and find the values of a, b, c , d and e. b + c + d + e = 4 a + c + d + e = 5 a + b + d + e = 1 a + b + c + e = 2 a + b. . . .

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In this interactivity each fruit has a hidden value. Can you deduce what each one is worth?

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Can you find the values at the vertices when you know the values on the edges?

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Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons?

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When I park my car in Mathstown, there are two car parks to choose from. Can you help me to decide which one to use?

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Which is bigger, n+10 or 2n+3? Can you find a good method of answering similar questions?

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You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.

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Can you work out how many of each kind of pencil this student bought?

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There is a particular value of x, and a value of y to go with it, which make all five expressions equal in value, can you find that x, y pair ?

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All CD Heaven stores were given the same number of a popular CD to sell for £24. In their two week sale each store reduces the price of the CD by 25% ... How many CDs did the store sell at. . . .

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There are lots of different methods to find out what the shapes are worth - how many can you find?

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The challenge is to find the values of the variables if you are to solve this Sudoku.

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Find all the triples of numbers a, b, c such that each one of them plus the product of the other two is always 2.

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You need to find the values of the stars before you can apply normal Sudoku rules.

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This is a variation of sudoku which contains a set of special clue-numbers. Each set of 4 small digits stands for the numbers in the four cells of the grid adjacent to this set.

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An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.

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Four numbers on an intersection that need to be placed in the surrounding cells. That is all you need to know to solve this sudoku.

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Solve the equations to identify the clue numbers in this Sudoku problem.

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Four jewellers share their stock. Can you work out the relative values of their gems?

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A, B & C own a half, a third and a sixth of a coin collection. Each grab some coins, return some, then share equally what they had put back, finishing with their own share. How rich are they?

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There are four children in a family, two girls, Kate and Sally, and two boys, Tom and Ben. How old are the children?

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Change one equation in this pair of simultaneous equations very slightly and there is a big change in the solution. Why?

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How many intersections do you expect from four straight lines ? Which three lines enclose a triangle with negative co-ordinates for every point ?

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Triangle ABC is an equilateral triangle with three parallel lines going through the vertices. Calculate the length of the sides of the triangle if the perpendicular distances between the parallel. . . .

Challenge Level

Show that for any triangle it is always possible to construct 3 touching circles with centres at the vertices. Is it possible to construct touching circles centred at the vertices of any polygon?

A simple method of defining the coefficients in the equations of chemical reactions with the help of a system of linear algebraic equations.

Challenge Level

How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?