This week's puzzle invites you to think in three dimensions about a fish navigating through a rectangular tank measuring two metres in height, one metre across, and one metre in depth.
The diagram below illustrates one particular route that the fish followed through the tank.
When this path is viewed from the front of the tank, from the right side, and from directly above, it produces three distinct two-dimensional projections shown in the images that follow.
What is the challenge?
Your task is to examine two separate puzzles, each presenting the front view and side view of different fish paths through the tank. Using only these two perspectives, you must determine what the top-down view of the shortest possible path would look like that could produce both of those projections.
Why is this puzzle so tricky?
Visualising three-dimensional shapes and paths from two-dimensional views requires spatial reasoning that many people find challenging. If you struggle with this type of mental rotation, architects are particularly well-suited to helping you work through it—they are trained specifically to interpret and construct three-dimensional spaces from multiple flat views. In fact, when similar puzzles were presented previously, architects were among the most enthusiastic solvers, recognising the connection to their professional training.
When will solutions be revealed?
The solutions to both puzzles will be posted at 5pm UK time today.
While you work on the challenge, the puzzle creator welcomes discussion of your favourite fish species—but please refrain from sharing your answers or hints that might spoil the puzzle for others.
Why this puzzle now?
These puzzles were designed by a maths educator to mark the opening of a new specialist mathematics secondary school, which will admit its first cohort of students later this month. Located in Mill Hill, north London, the institution represents a significant milestone as the first dedicated maths secondary school to launch in the United Kingdom. Its name draws inspiration from a celebrated historical anecdote.
The puzzle series has been a regular feature since 2015, appearing on alternate Mondays. If you have discovered an engaging puzzle you believe would work well for this column, you are encouraged to submit suggestions by email.
