An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Choose any three by three square of dates on a calendar page...
Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
An ant crawls carefully around the edges of a cube, starting at point $P$ and in the direction of the arrow.
At the end of the first edge it chooses whether to go either left or right. It then turns the other way at the end of the next edge and continues like this, turning right or left alternately at the end of each successive edge.
After how many edges does the ant return to point $P$ for the first time?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
This problem is taken from the UKMT Mathematical Challenges.