Here are three counting puzzles from Alex Bellos’s book, Can You Solve My Problems? Bellos recalls the famous legend of the young Gauss in the 19th century who summed up the whole numbers from 1 to 100 by finding a pattern that would simplify the work. Bellos also mentioned that Alcuin some thousand years earlier had discovered a similar, but different, pattern to sum up the numbers. In presenting these three problems he said, “The lesson … is this: If you’re asked to add up a whole bunch of numbers, don’t undertake the challenge literally. Look for the pattern and use it to your advantage.”
See Three Counting Puzzles for solutions.
The craziness of manipulating radicals strikes again. This 2006 four-star problem from Colin Hughes at Maths Challenge is really astonishing, though it takes the right key to unlock it.
Again we have a puzzle from the Sherlock Holmes puzzle book by Dr. Watson (aka Tim Dedopulos).
This is a cute little problem I came across via 
This is a nice variation on the typical clock problem posed by 
Here is another good problem from Five Hundred Mathematical Challenges:
This is another challenging puzzle from 
I thought it would be interesting to present a recent entry in the mathematician John Baez’s Diary on some extremes in mathematics from the Bourbaki school, namely, how many symbols it would take to define the number “1.”
Here is another problem from the 2020 Math Calendar to stimulate your mind.
