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Diophantine equations. Interactivities. Indices. Multiplication & division. Mathematical reasoning & proof. Simultaneous equations. Working systematically. Other equations. Powers & roots. Creating and manipulating expressions and formulae.There are 14 results
Broad Topics > Algebraic expressions, equations and formulae > Diophantine equations
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?
Hallway Borders
Age 11 to 14 Challenge Level:
What are the possible dimensions of a rectangular hallway if the number of tiles around the perimeter is exactly half the total number of tiles?
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?
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. . . .
Not a Polite Question
Age 11 to 14 Short Challenge Level:
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...
Deep Roots
Age 14 to 16 Challenge Level:
Find integer solutions to: $\sqrt{a+b\sqrt{x}} + \sqrt{c+d.\sqrt{x}}=1$
Letter Land
Age 11 to 14 Challenge Level:
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.
Our Ages
Age 14 to 16 Challenge Level:
I am exactly n times my daughter's age. In m years I shall be ... How old am I?
Whole Numbers Only
Age 11 to 14 Short Challenge Level:
Can you work out how many of each kind of pencil this student bought?
In Particular
Age 14 to 16 Challenge Level:
Can you find formulas giving all the solutions to 7x + 11y = 100 where x and y are integers?
Are You Kidding
Age 14 to 16 Challenge Level:
If the altitude of an isosceles triangle is 8 units and the perimeter of the triangle is 32 units.... What is the area of the triangle?
Upsetting Pitagoras
Age 14 to 18 Challenge Level:
Find the smallest integer solution to the equation 1/x^2 + 1/y^2 = 1/z^2
Plutarch's Boxes
Age 11 to 14 Challenge Level:
According to Plutarch, the Greeks found all the rectangles with integer sides, whose areas are equal to their perimeters. Can you find them? What rectangular boxes, with integer sides, have. . . .
Fibs
Age 11 to 14 Challenge Level:
The well known Fibonacci sequence is 1 ,1, 2, 3, 5, 8, 13, 21.... How many Fibonacci sequences can you find containing the number 196 as one of the terms?
NRICH is part of the family of activities in the Millennium Mathematics Project.