I totally agree with this. About a month ago I created a site that puts up a new programming or logic puzzle every day Monday-Friday. The exercises usually take no more than 30min and the community has been steadily growing. If you're interested you can check it out at http://problemotd.com/
Something similar can be found at Project Euler, http://projecteuler.net/ or at Codewars, http://www.codewars.com/, although those have a stricter format than your examples. For example, the challenges at Project Euler all have a single number as answer. Some problems can thus be solved via mathematics, but for most a program -- you may pick the language -- is most efficient.
