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?
Three semi-circles have a common diameter, each touches the other
two and two lie inside the biggest one. What is the radius of the
circle that touches all three semi-circles?
Label this plum tree graph to make it totally magic!
The numbers $2$, $34$ and $47$ are such that the sum of any pair
of these numbers is a perfect square. Find a method for choosing
three square numbers and from them finding a corresponding set of
three integers with this property and give some examples.
The integers $-208$, $224$, $352$ and $737$ also have the
property that the sum of any pair of these numbers is a perfect
square. Find other sets of four integers with this property.