Combinatorics

A personal investigation of Conway's Rational Tangles. What were the interesting questions that needed to be asked, and where did they lead?

Sanjay Joshi, age 17, The Perse Boys School, Cambridge followed up the Madrass College class 2YP article with more thoughts on the problem of the number of ways of expressing an integer as the sum of odd numbers.

A big prize was offered for solving The Eternity Puzzle, a jigsaw with no picture and every piece is the same on both sides. The finished result forms a regular dodecagon (12 sided polygon).

Suppose A always beats B and B always beats C, then would you expect A to beat C? Not always! What seems obvious is not always true. Results always need to be proved in mathematics.

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.