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?
After every two numbers, one is omitted. Because $89 = 2\times 44 +1$, there must be $44$ page numbers missing and so the number on the last page is $89+44=133$.
This problem is taken from the UKMT Mathematical Challenges.