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?
Buying two more parsnips and three fewer turnips does not change the total cost and hence two parsnips cost the same as three turnips. Instead of six parsnips therefore, Baldrick could have bought nine turnips, and together with seven turnips, this makes a total of 16 turnips. Alternatively he could have bought twelve turnips instead of eight parsnips and , together with four turnips, this
makes sixteen turnips.
This problem is taken from the UKMT Mathematical Challenges.