Choose any three by three square of dates on a calendar page...
Make a set of numbers that use all the digits from 1 to 9, once and
once only. Add them up. The result is divisible by 9. Add each of
the digits in the new number. What is their sum? Now try some other
possibilities for yourself!
What happens to the perimeter of triangle ABC as the two smaller
circles change size and roll around inside the bigger circle?
The last ten Flibbins who live on the planet Filbert are in trouble. They are under threat from a cactus-like creature whose spines are fatal to the Flibbins and who are due to start their annual moult in a few days time!!
The Flibbins have found a neighbouring planet that is uninhabited and where they can survive if they can get there safely. However, they have some problems with organising their emigration.
Firstly, they only have one spacecraft that will carry at most one pilot and two passengers. Of course, the spacecraft can't fly (either to the new planet or back from it) without a pilot, which can be any of the Flibbins!
Secondly, the ten Flibbins each have a partner of the opposite colour. The blue Flibbins are all very protective of their red partners, so if the blue partner is not present (on either planet or the spacecraft), there should be no other blue Flibbins with their red partner (but other red Flibbins are fine). Red Flibbins, however, are not so protective of their blue partners.
What is the quickest way of getting the five pairs of Flibbins safely to the new planet?