# Resources tagged with: Other equations

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There are 21 NRICH Mathematical resources connected to Other equations, you may find related items under Algebraic expressions, equations and formulae.

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

### One and Three

##### Age 14 to 16Challenge Level

Two motorboats travelling up and down a lake at constant speeds leave opposite ends A and B at the same instant, passing each other, for the first time 600 metres from A, and on their return, 400. . . .

### Root to Poly

##### Age 14 to 16Challenge Level

Find the polynomial p(x) with integer coefficients such that one solution of the equation p(x)=0 is $1+\sqrt 2+\sqrt 3$.

### Polynomial Relations

##### Age 16 to 18Challenge Level

Given any two polynomials in a single variable it is always possible to eliminate the variable and obtain a formula showing the relationship between the two polynomials. Try this one.

### N Is a Number

##### Age 11 to 14Challenge Level

N people visit their friends staying N kilometres along the coast. Some walk along the cliff path at N km an hour, the rest go by car. How long is the road?

### Golden Ratio

##### Age 16 to 18Challenge Level

Solve an equation involving the Golden Ratio phi where the unknown occurs as a power of phi.

### Top-heavy Pyramids

##### Age 11 to 14Challenge Level

Use the numbers in the box below to make the base of a top-heavy pyramid whose top number is 200.

### 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: $\sqrt{a+b\sqrt{x}} + \sqrt{c+d.\sqrt{x}}=1$

### Around and Back

##### Age 14 to 16Challenge Level

A cyclist and a runner start off simultaneously around a race track each going at a constant speed. The cyclist goes all the way around and then catches up with the runner. He then instantly turns. . . .

### 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. . . .

### Three Four Five

##### Age 14 to 16Challenge Level

Two semi-circles (each of radius 1/2) touch each other, and a semi-circle of radius 1 touches both of them. Find the radius of the circle which touches all three semi-circles.

### Hike and Hitch

##### Age 14 to 16Challenge Level

Fifteen students had to travel 60 miles. They could use a car, which could only carry 5 students. As the car left with the first 5 (at 40 miles per hour), the remaining 10 commenced hiking along the. . . .

### How Big?

##### Age 11 to 14Challenge Level

If the sides of the triangle in the diagram are 3, 4 and 5, what is the area of the shaded square?

### Hand Swap

##### Age 14 to 16Challenge Level

My train left London between 6 a.m. and 7 a.m. and arrived in Paris between 9 a.m. and 10 a.m. At the start and end of the journey the hands on my watch were in exactly the same positions but the. . . .

### 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?

### 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?

### Old Nuts

##### Age 16 to 18Challenge Level

In turn 4 people throw away three nuts from a pile and hide a quarter of the remainder finally leaving a multiple of 4 nuts. How many nuts were at the start?

### 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?

### Building Tetrahedra

##### Age 14 to 16Challenge Level

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

### Real(ly) Numbers

##### Age 16 to 18Challenge 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?