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 number may be divided up into 400 blocks of '12345'. The sum
of the digits in each block is 15 and there are 400 blocks. Hence
the sum of all 2000 digits is 400 x 15 = 6000.
Alternatively, the mean of each group of five digits is 3 and so
the mean of the digits making up the number is 3. Therefore the sum
is 2000x3 = 6000.
This problem is taken from the UKMT Mathematical Challenges.