Show that the infinite set of finite (or terminating) binary
sequences can be written as an ordered list whereas the infinite
set of all infinite binary sequences cannot.
Draw a 'doodle' - a closed intersecting curve drawn without taking pencil from paper. What can you prove about the intersections?
Nowadays the calculator is very familiar to many of us. What did
people do to save time working out more difficult problems before
the calculator existed?
Follow-up to the February Game Rules of FEMTO.
A game for two people, who take turns to move the counters. The player to remove the last counter from the board wins.
The interval 0 - 1 is marked into halves, quarters, eighths ...
etc. Vertical lines are drawn at these points, heights depending on
positions. What happens as this process goes on indefinitely?
A new card game for two players.
Solve this Sudoku puzzle whose clues are in the form of sums of the
numbers which should appear in diagonal opposite cells.
Some puzzles requiring no knowledge of knot theory, just a careful inspection of the patterns. A glimpse of the classification of knots, prime knots, crossing numbers and knot arithmetic.
How many different ways can you arrange the officers in a square?
Some relationships are transitive, such as `if A>B and B>C
then it follows that A>C', but some are not. In a voting system,
if A beats B and B beats C should we expect A to beat C?