Four jewellers share their stock. Can you work out the relative values of their gems?
One night two candles were lit. Can you work out how long each candle was originally?
Take any rectangle ABCD such that AB > BC. The point P is on AB and Q is on CD. Show that there is exactly one position of P and Q such that APCQ is a rhombus.
What's the most efficient proportion for a 1 litre tin of paint?
A square is divided into four rectangles and a square. Can you work out the ratio of the side lengths of the rectangles?
Using an understanding that 1:2 and 2:3 were good ratios, start with a length and keep reducing it to 2/3 of itself. Each time that took the length under 1/2 they doubled it to get back within range.
Two perpendicular lines lie across each other and the end points are joined to form a quadrilateral. Eight ratios are defined, three are given but five need to be found.
Does Joseph have too many sheep in his flock...
Andy is desperate to reach John o'Groats first. Can you devise a winning race plan?
Straight lines are drawn from each corner of a square to the mid points of the opposite sides. Express the area of the octagon that is formed at the centre as a fraction of the area of the square.
