Other tags that relate to Diverging
Working systematically. Generalising. Mathematical reasoning & proof. Making and proving conjectures. Inequalities. Simultaneous equations. Creating and manipulating expressions and formulae. Graphs. Polynomial functions and their roots. Indices.There are 40 results
Broad Topics > Algebraic expressions, equations and formulae > Simultaneous equations
Quadratic Harmony
Age 16 to 18 Challenge Level:
Find all positive integers a and b for which the two equations: x^2-ax+b = 0 and x^2-bx+a = 0 both have positive integer solutions.
Leonardo's Problem
Age 14 to 18 Challenge Level:
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?
Pair Squares
Age 16 to 18 Challenge Level:
The sum of any two of the numbers 2, 34 and 47 is a perfect square. Choose three square numbers and find sets of three integers with this property. Generalise to four integers.
System Speak
Age 16 to 18 Challenge Level:
Five equations... five unknowns... can you solve the system?
Matchless
Age 14 to 16 Challenge Level:
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 ?
All-variables Sudoku
Age 11 to 18 Challenge Level:
The challenge is to find the values of the variables if you are to solve this Sudoku.
Double Time
Age 16 to 18 Challenge Level:
Crack this code which depends on taking pairs of letters and using two simultaneous relations and modulus arithmetic to encode the message.
Multiplication Arithmagons
Age 14 to 16 Challenge Level:
Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons?
Gift of Gems
Age 14 to 16 Challenge Level:
Four jewellers share their stock. Can you work out the relative values of their gems?
Always Two
Age 14 to 18 Challenge Level:
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.
Arithmagons
Age 14 to 16 Challenge Level:
Can you find the values at the vertices when you know the values on the edges?
Simultaneous Equations Sudoku
Age 11 to 16 Challenge Level:
Solve the equations to identify the clue numbers in this Sudoku problem.
Real(ly) Numbers
Age 16 to 18 Challenge Level:
If x, y and z are real numbers such that: x + y + z = 5 and xy + yz + zx = 3. What is the largest value that any of the numbers can have?
Quadruple Clue Sudoku
Age 11 to 16 Challenge Level:
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.
Another Quadruple Clue Sudoku
Age 11 to 16 Challenge Level:
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.
LCM Sudoku II
Age 11 to 18 Challenge Level:
You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.
Which Is Cheaper?
Age 14 to 16 Challenge Level:
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?
Warmsnug Double Glazing
Age 14 to 16 Challenge Level:
How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?
Which Is Bigger?
Age 14 to 16 Challenge Level:
Which is bigger, n+10 or 2n+3? Can you find a good method of answering similar questions?
Fruity Totals
Age 7 to 16 Challenge Level:
In this interactivity each fruit has a hidden value. Can you deduce what each one is worth?
Overturning Fracsum
Age 14 to 16 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
CD Heaven
Age 14 to 16 Challenge Level:
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. . . .
Building Tetrahedra
Age 14 to 16 Challenge Level:
Can you make a tetrahedron whose faces all have the same perimeter?
Polycircles
Age 14 to 16 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?
Surds
Age 14 to 16 Challenge Level:
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
Coffee
Age 14 to 16 Challenge Level:
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?
Rudolff's Problem
Age 14 to 16 Challenge Level:
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?
Negatively Triangular
Age 14 to 16 Challenge Level:
How many intersections do you expect from four straight lines ? Which three lines enclose a triangle with negative co-ordinates for every point ?
What's it Worth?
Age 11 to 16 Challenge Level:
There are lots of different methods to find out what the shapes are worth - how many can you find?
Pareq Calc
Age 14 to 16 Challenge Level:
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. . . .
Graphs of Changing Areas
Age 16 to 18 Challenge Level:
Use graphs to gain insights into an area and perimeter problem, or use your knowledge of area and perimeter to gain insights into the graphs...
Escriptions
Age 16 to 18 Challenge Level:
For any right-angled triangle find the radii of the three escribed circles touching the sides of the triangle externally.
Intersections
Age 14 to 18 Challenge Level:
Change one equation in this pair of simultaneous equations very slightly and there is a big change in the solution. Why?
A Method of Defining Coefficients in the Equations of Chemical Reactions
Age 14 to 18
A simple method of defining the coefficients in the equations of chemical reactions with the help of a system of linear algebraic equations.
How Many Balls?
Age 16 to 18 Challenge Level:
A bag contains red and blue balls. You are told the probabilities of drawing certain combinations of balls. Find how many red and how many blue balls there are in the bag.
Walls
Age 16 to 18 Challenge Level:
Plane 1 contains points A, B and C and plane 2 contains points A and B. Find all the points on plane 2 such that the two planes are perpendicular.
Cobalt Decay
Age 16 to 18 Challenge Level:
Investigate the effects of the half-lifes of the isotopes of cobalt on the mass of a mystery lump of the element.
NRICH is part of the family of activities in the Millennium Mathematics Project.