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?
Consider numbers whose fist digit is 1. Looking at each possible
value for the second digit we find 9 such numbers.
110, 121, 132, 143, 154, 165, 176, 187, 198.
Similarly there are 8 numbers starting with 2; 7 numbers
starting with 3...
Lastly there is only one number starting with 9: 990.
Hence the total is 9+8+7+6+5+4+3+2+1 = 45.
This problem is taken from the UKMT Mathematical Challenges.View the archive of all weekly problems grouped by curriculum topic