An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
What is the smallest number with exactly 14 divisors?
Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?
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 he chooses to go either left or right. He 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.