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?
Liam's house has a staircase with $12$ steps. He can go down the steps one at a time or two at a time.
For example, he could go down $1$ step, then $1$ step, then $2$ steps, then $2$, $2$, $1$, $1$, $1$, $1$.
In how many different ways can Liam go down the $12$ steps, taking one or two steps at a time?