Are you ready for a brain teaser that connects geometry, transport links, and a bit of soapy magic? Today's puzzle challenges you to find the most efficient road system to connect four towns arranged at the corners of a square.
The Four Towns Challenge
Four towns are positioned at each corner of a perfect square. Your task is to design a road network that links all four settlements using the smallest total length of tarmac. It sounds simple, but the obvious answers are surprisingly inefficient.
The O-loop, which creates a continuous road around the square, uses too much unnecessary asphalt. The U-route, connecting three towns in a U-shape before reaching the fourth, is also needlessly lavish. Even the direct X-road, which crisscrosses between opposite corners, isn't the optimal solution for minimising overall road length.
Nature's Ingenious Solution
Rather than relying on complex mathematics, you can solve this problem using a remarkable analogue computer: soap bubbles. If you create a physical model of the puzzle using two transparent plates with four equal-length dowels positioned at the square's corners and dip it into soapy water, the bubbles that form will instantly reveal the minimal structure.
Nature consistently finds the most efficient path, and in this case, the solution resembles a simple geometrical shape that appears frequently in the real world. The soap bubble demonstration provides a stunning visual proof of the mathematical principle at work.
Where Maths Comes to Life
This fascinating puzzle was recently highlighted at MathsWorld London, the capital's first attraction dedicated entirely to mathematics. Located just minutes from the Tate Modern in Southwark, this new discovery centre features dozens of interactive exhibits that bring mathematical concepts to life through play.
One of the most popular attractions is the gigantic soap bubble machine, where visitors can stand inside and pull a massive bubble over their heads. Other exhibits include an elliptical pool table, a Morse code machine, a five-foot build-your-own arch, and numerous hands-on puzzles.
MathsWorld London represents the culmination of years of planning and fundraising, creating an inclusive and joyous space that makes mathematics accessible to all. For those outside the capital, a similar giant bubble machine can be found at MathsCity Leeds, which has been operating since 2021.
Both venues demonstrate how mathematical principles surround us in everyday life, from the efficient patterns formed by soap bubbles to the optimal paths between connected points. The four towns puzzle serves as a perfect example of how nature often holds the solutions to complex problems.
