Take ten sticks in heaps any way you like. Make a new heap using one from each of the heaps. By repeating that process could the arrangement 7 - 1 - 1 - 1 ever turn up, except by starting with it?
On a "move" a stone is removed from two of the circles and placed
in the third circle. Here are five of the ways that 27 stones could
Take any pair of numbers, say 9 and 14. Take the larger number,
fourteen, and count up in 14s. Then divide each of those values by
the 9, and look at the remainders.
Find all the periodic cycles and fixed points in this number
sequence using any whole number as a starting point.
A spiropath is a sequence of connected line segments end to end
taking different directions. The same spiropath is iterated. When
does it cycle and when does it go on indefinitely?
Analyse these repeating patterns. Decide on the conditions for a
periodic pattern to occur and when the pattern extends to infinity.
Here is an easy proof of the Cauchy Schwarz inequality.
Go to last month's problems to see more solutions.
This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
A Sudoku based on clues that give the differences between adjacent cells.