# Resources tagged with: Diophantine equations

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There are 14 NRICH Mathematical resources connected to Diophantine equations, you may find related items under Algebraic expressions, equations and formulae.

Broad Topics > Algebraic expressions, equations and formulae > Diophantine equations

### Letter Land

##### Age 11 to 14Challenge 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.

### CD Heaven

##### Age 14 to 16Challenge 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. . . .

### Fibs

##### Age 11 to 14Challenge 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?

### Are You Kidding

##### Age 14 to 16Challenge 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?

### Deep Roots

##### Age 14 to 16Challenge Level

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

### Plutarch's Boxes

##### Age 11 to 14Challenge 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. . . .

### In Particular

##### Age 14 to 16Challenge Level

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

### Whole Numbers Only

##### Age 11 to 14 ShortChallenge Level

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

### Not a Polite Question

##### Age 11 to 14 ShortChallenge 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...

### Coffee

##### Age 14 to 16Challenge 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?

### Hallway Borders

##### Age 11 to 14Challenge 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?

### Our Ages

##### Age 14 to 16Challenge Level

I am exactly n times my daughter's age. In m years I shall be ... How old am I?

### Rudolff's Problem

##### Age 14 to 16Challenge Level

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

### Upsetting Pitagoras

##### Age 14 to 18Challenge Level

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