problem

### N is a Number

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?

problem
###
N is a Number

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?

problem
###
Golden Ratio

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

problem
###
Top-Heavy Pyramids

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

problem
###
Are you kidding

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?

problem
###
Around and Back

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 around and heads back to the starting point where he meets the runner who is just finishing his first circuit. Find the ratio of their speeds.

problem
###
Plutarch's Boxes

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 their
surface areas equal to their volumes?

problem
###
Three four five

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.

problem
###
Hike and Hitch

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 road (at 4 miles per hour)...

problem
###
How big?

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