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? The diagram shows the first three
patterns in a sequence in which each pattern has a square hole
in the middle. How many small shaded squares are needed to build
the tenth pattern in the sequence? 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.