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?
Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
The diagram show the net of a regular octohedron.
In a Magic Octahedron, the four numbers on the faces that meet at a vertex add up to make the same total for every vertex. If the letters $F, G, H, J$ and $K$ are replaced with the numbers $2, 4, 6, 7$ and $8$, in some order, to make a Magic Octohedron, what is the value of $G + J$?
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.