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?
Let the athlete take x minutes to cycle one mile.
Therefore he takes 3x/2 minutes to run one mile and
3x minutes to walk one mile.
Therefore 3x +3x/2 +x = 3x + 10 i.e. x = 4
The cyclist takes 12 minutes to walk the first mile, 6 minutes to run the second mile and 4 minutes to cycle the third mile, a total time of 22 minutes.
This problem is taken from the UKMT Mathematical Challenges.