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?
Investigate how you can work out what day of the week your birthday
will be on next year, and the year after...
This problem is taken from the UKMT Mathematical Challenges.