As the year draws to a close, many of us find ourselves contemplating what the future holds, especially when it comes to numbers.
The Unique Year 2025
Among the years that will soon come, 2025 stands out as a unique gem: it is the only square number we will see in this century.
To illustrate, consider these calculations:
442 = 1936
452 = 2025
462 = 2116
What’s particularly intriguing is that the number 45 can be broken down into 20 + 25, allowing us to create the elegant expression:
(20 + 25)2 = 2025
Furthermore, 2025 is noteworthy as it will be the first year in the five times table since 1520, making it a historic mark on the calendar.
Challenge: Queens and Pawns
I recently reached out to Inder Taneja, a retired mathematician with a knack for spotting numerical patterns, to share some fascinating tidbits about the number 25.
Among his insights was a remarkable equation that remains consistent at 25 whether read in its normal orientation, flipped, or reflected.
Today, I present you with an engaging challenge involving a grid of 25 squares.
Challenge: Queens and Pawns
Your mission is to strategically position five queens and three pawns on the grid.
The key is to ensure that none of the queens can attack any of the pawns.
A queen moves in straight lines—horizontally, vertically, and diagonally—so this task is all about finding the right arrangement for these chess pieces so they maintain their distance from three designated cells.
I’ve devised a method to place four queens effectively, yet the challenge intensifies when you try to add a fifth queen into the mix, which is trickier than it first appears.
Challenge: Christmas Star
Let’s dive into another fascinating puzzle connected to the number five: the five-pointed star.
This geometric wonder is composed of five triangles.
Your goal is to draw just two straight lines, resulting in a figure that showcases ten distinct triangles.
Remember to count only those triangles that are not crossed by any lines—it’s a straightforward task with no hidden twists!
I’ll return at √25 pm (UK time) to share the solutions.
I kindly ask that you hold off on revealing any answers until then.
Instead, I’d love to hear your favorite stories or anecdotes associated with the number 25.
A big thanks to Chris Smith for introducing me to the queens and pawns puzzle.
Also, gratitude goes to Inder Jeet Taneja, who shared his insightful paper titled Reflexive Year 25: Mathematics of 25 and 2025 in Numbers and Magic Squares, published on Zenodo in December 2024.
Since 2015, I’ve been sharing puzzles every other Monday, and I’m always on the lookout for fresh and exciting challenges.
If you have a puzzle in mind, don’t hesitate to drop me an email at bellospuzzle@gmail.com.
And for those of you scrambling for last-minute gift ideas, my book, Think Twice: Solve The Simple Puzzles (Almost) Everyone Gets Wrong, is now available!
Source: The guardian