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 a solid with six triangular faces. At each vertex there is a number and two of the numbers are 1 and 5, as shown. The sum of the numbers at the three vertices of each face is calculated, and all the sums are the same. What is the sum of all five numbers at the vertices?
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.