Guardian reveals solution to its geometric fish-tank puzzle

The Guardian newspaper has shared the answers to two geometry puzzles it recently posed to readers in its regular puzzle column, both based on a fish swimming inside a rectangular tank measuring two metres high, one metre wide and one metre deep.

Readers were shown one path the fish swam, illustrated from the front, the side and from above, and were then given two further examples of front and side views. The challenge was to work out the shortest possible path matching each pair of views and to sketch what that path would look like from above.

How the puzzles were solved

For the first puzzle, the solution depended on identifying a specific vertical cross-section of the tank on which parts of the path had to lie, with the final segment confined to a particular shaded area. For the second puzzle, the lower and upper portions of the path each had to sit within their own distinct cross-sections, and because the shortest possible route was required, there was only one way to connect the two halves and complete the path across the top of the tank.

Puzzle tied to new school launch

The puzzles were devised by maths educator George Watkins to celebrate the opening of the 1729 Maths School in Mill Hill, north London. The school, which is due to welcome its first students later this month, is described as the first specialist maths secondary school in the UK.

Its name references the well-known anecdote about a London taxicab bearing the licence plate 1729, a number with a notable place in number theory. The Guardian's puzzle column, running on alternate Mondays since 2015, continues to invite readers to submit puzzle suggestions for future editions.