Can you solve it? All you need to know about 2025

New Year's Eve 2025 numerals arrive in Times Square in Photograph: Sarah Yenesel/EPA

As is traditional for the final column of year, we look ahead to all that the following twelve months will bring us.

Numerically speaking, of course.

2025 will be the only time this century that the year is a square number.

• 44² = 1936

• 45² = 2025

• 46² = 2116

In fact, since 45 = 20 + 25, we have the very nice equation:

(20 + 25)² = 2025

2025 is also the first year since 1520 that appears in the five times table. It has been a long wait.

I asked Inder Taneja, a retired maths professor who looks for amusing patterns in numbers, for some fun ‘25’ facts. He sent me the following sum, which is equal to 25 whether you read it the right way up, or upside down, or in the mirror, or upside down in the mirror.

Today’s first puzzle is about a grid with 25 squares.

Queens and pawns

Place five queens and three pawns in the grid so that no queen is attacking a pawn.

A queen can move horizontally, vertically or diagonally. So, for those unfamiliar with the rules of the chess, the puzzle is asking you to place five pieces in the grid in such a way that there are exactly three cells these pieces cannot move to, horizontally, vertically or diagonally.

Here’s a way to place four queens. But can you add a fifth? The puzzle is much harder than it looks (or it was for me.)

Christmas star

Another puzzle that is much harder than it looks, and involves a 5, and is a bit festive, is this old chestnut (roasting on an open fire). There are 5 triangles in this five pointed star. Can you draw two straight lines through the star to create an image with 10 triangles? For this puzzle, only triangles that have no lines running though them count as triangles. And it is not a trick question – there is a simple way to do it!

I’ll be back at √25 pm UK with the solutions.

UPDATE: Solutions are up here.

Please NO SPOILERS, instead please share your favourite stories about the number 25.

Thanks to Chris Smith, who first showed me the queens and pawns puzzle, and to Inder Jeet Taneja. His paper on 2025 is Reflexive Year 25: Mathematics of 25 and 2025 in Numbers and Magic Squares, Zenodo, December 20, 2024,pp. 1-94.

I’ve been setting a puzzle here on alternate Mondays since 2015. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.

Looking for a last minute stocking filler? Think Twice , Solve The Simple Puzzles (Almost) Everyone Gets Wrong is my latest book.