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 numbers along the leading diagonal total 58, which is
therefore the sum of each row and each column. We can now calculate
that the number to the left of 10 must be 20 and below that must be
7. Hence x=21
This problem is taken from the UKMT Mathematical Challenges.View the archive of all weekly problems grouped by curriculum topic