Can you solve it? Are you smarter than a soap bubble? | mathematics
Today’s puzzle revolves around transportation lines, water, and soap.
The four cities
Four cities lie on the corners of the square, as follows:
What is the road system that connects the four cities using the smallest total road length?
Here is the wrong answer. The O-ring uses a lot of unnecessary asphalt.
The U-road is also unnecessarily luxurious.
Route
Can you tell what the lower road network looks like?
I don’t expect you to solve this problem mathematically, that would require very complex techniques. But you may be able to make an intuitive guess.
Alternatively, you can solve this problem by using soap bubbles. If you make a plastic model of the puzzle (a sandwich where the “bread” is two pieces of flat, transparent material and the “filling” is four short nails of equal length, placed in the corners of a square) and place it in a bowl of soapy water, bubbles will form around the nails to display the answer.
Nature finds minimal structure immediately. The plastic model looks like an analog computer. In fact, here’s a hint: The solution looks like a simple geometric shape that appears in the real world in a very familiar environment.
I’ll be back at 5pm UK with the answer and a video of the soap bubble solution.
Please don’t spoil, please discuss your favorite bubbles.
I’ve been meaning to share this puzzle for a long time, and was reminded of it recently when I went to MathsWorld London, a maths discovery center that has just opened in Southwark, a few minutes’ walk from the Tate Modern.
The place has dozens of interactive exhibits, and one of my kids’ favorites was the giant soap bubble machine. You stand in it and pull a bubble over your heads.
Other exhibits include an oval-shaped pool table, a Morse code machine, a 5-foot bow, and several practical puzzles.
MathsWorld London is the capital’s first attraction with a unique focus on mathematics and was the culmination of years of planning and fundraising. Each exhibit reflects some mathematical idea through gameplay, with an explanation on hand if you want to learn more. It’s a wonderfully inclusive and colorful space, and a welcome addition to London’s cultural scene.
If you don’t live in London, there’s also a giant bubble machine at MathsCity Leeds, a sister project to MathsWorld London which has been running since 2021.
London mathematician He is At 6 Burrell Street, London, SE1 0UN.
Maths City Leeds Located at Zurich House, 4 Canal Wharf, Leeds, LS11 5PS.
I’ve been doing puzzle here on Alternate Mondays since 2015. I’m always on the lookout for great puzzles. If you would like to suggest one, email me.