As the curtain falls on 2025, mathematicians and puzzle enthusiasts across the UK are taking a final, fond look at a year that was truly unique in numerical terms. The year just passed held a special distinction this century: it was a perfect square number.
A Square Year to Remember
The sequence of square numbers around our recent calendar reveals the charm: 44 squared equals 1936, 45 squared gives us 2025, and 46 squared will be 2116. The delight didn't end there. Observant minds marvelled at a dazzling additional pattern, noting that 45 itself breaks down into 20 and 25, leading to the elegant equation: (20 + 25)² = 2025. It was a brief, beautiful moment of numerical symmetry.
But time marches on, and so does the calendar. The question now is: what does 2026 have in store? The answer, in playful terms, is "six seven!" – a nod to the digits that will define the new year's puzzles.
The Auld Lang Signs Challenge
Puzzle setter Alex Bellos, who has been offering fortnightly brainteasers since 2015, has ushered in 2026 with a fresh numerical challenge. He starts by showing how the number 26 can be crafted using six 1s: (1+1) × (1+1+11).
The new year's puzzle asks solvers to find expressions equal to 26 using different sets of digits. The challenge is to create valid equations using:
- Five 9s
- Six 8s
- Six 7s
- Six 6s
- Four 5s
- Six 4s
- Four 3s
- Four 2s
The rules are specific. Participants may only use the four basic operations (addition, subtraction, multiplication, division), brackets, exponentiation (like making a digit an exponent, e.g., 1¹), and concatenation (joining digits together, such as making '11' from two 1s). The playful mention of "a partridge in a pear tree" is, of course, just a festive joke.
Celebrating the Number 26
While solutions to the puzzle will be revealed at 5pm UK time, Bellos encourages readers to share their favourite facts about the number 26 instead of posting spoilers. This engaging approach keeps the community spirit alive and celebrates the beauty of numbers themselves.
The puzzle draws inspiration from the work of Inder Taneja, author of the website numbers-magic.com. Taneja has explored the coming year in depth in his paper "26 and 2026 in Numbers and Magic Squares", which is filled with many more numerical facts and curiosities.
For those with a passion for puzzles, Alex Bellos continues to seek out great challenges. He invites suggestions to be sent directly to him via email, maintaining a vibrant and collaborative space for mathematical discovery.
