# Resources tagged with: Diophantine equations

### There are 14 results

Broad Topics >

Algebraic expressions, equations and formulae > Diophantine equations

##### 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...

##### 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?

##### 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?

##### 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?

##### Age 11 to 14 Short

Challenge Level

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

##### 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?

##### Age 14 to 16

Challenge Level

Find integer solutions to: $\sqrt{a+b\sqrt{x}} + \sqrt{c+d.\sqrt{x}}=1$

##### 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.

##### Age 14 to 16

Challenge Level

Can you find formulas giving all the solutions to 7x + 11y = 100 where x and y are integers?

##### 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. . . .

##### 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?

##### Age 14 to 18

Challenge Level

Find the smallest integer solution to the equation 1/x^2 + 1/y^2 = 1/z^2

##### 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?

##### 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. . . .