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?
$35$ teenagers were asked what takeaways they liked to eat.
None of the teenagers liked all three. All who liked pizza also liked Chinese and $9$ of the Chinese fans didn't like either Indian or pizza.
If all the teenagers liked at least one, how many liked only Indian?
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.