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?
A wooden cube has three of its faces painted red and the other three of its faces painted blue. It is then cut into $27$ identical smaller cubes. How many of these new cubes have at least one red face and also at least one blue face?
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.