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?
In Emily's first spelling test of this new term she scored one mark out of five, so she decided to work really hard to improve her scores. Assuming that she succeeds on scoring full marks in all her tests after the first, how many more tests does she need to take to increase her average to more than $80$%.
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.