Can you solve it? The magnificent Grabarchuks, Ukraine’s puzzle family | Mathematics

Today’s puzzles are all about helping Ukraine.

They are written by the Grabarchuk family, who are one of the world’s most original and prolific puzzle creators. Originally from the Western Ukrainian city of Uzhgorod, on the Slovakian border, the family moved to the USA in 2013 on the back of becoming internationally renowned for their puzzle books, websites and apps. Computer science legend Donald Knuth says that Serhiy Grabarchuk, the father of the clan, “has my vote as the world’s current puzzle laureate. His works are particularly beautiful, instructive and fulfilling.”

Since the beginning of the war, the Grabarchuks have been publishing a daily puzzle that promotes Ukrainian culture (such as the ‘spot the difference’ of St Sophia’s Cathedral at the top of this story) hoping to raise money for humanitarian and military aid.

Below are six puzzles I selected from the family’s archive. If you enjoy them please consider contributing to their suggested causes. Slava Ukraini!

1. Hex vex

Which digit should replace the question mark?

2. Ring ding

Which system of rings differs from the others?


3. Snake shake

Which view of the 11-cube snake is incorrect?


4. Box fox

Put a digit in each box so all 8 equations, across and down, are all correct. One box already has a digit.

This puzzle was created in collaboration with Harry Nelson
This puzzle was created in collaboration with Harry Nelson

5. Sign mine

Which of the signs in the bottom row should replace the question mark?


6. Ele-mental

For each of these six elements, find another element that has no letter in common with its counterpart. Each answer is unique.

Created in collaboration with Donald Knuth

Hint: all the answers are well-known elements, words that are in a non-chemist’s vocabulary.

NO SPOILERS. I’ll be back at 5pm UK with the answers.

UPDATE: Read the solutions here.

The Grabarchuk story began five decades ago when Serhiy, now aged 64, was a schoolboy in Uzhgorod. He discovered a talent for making puzzles and magic tricks, and turned it into a career. By the 1990s he and his wife Tanya had a small company publishing puzzle books, and now the business has expanded to websites and apps and involves his sons, Serhiy Jr and Peter, and their wives, Kate and Helen. The family’s most successful puzzle is Strimko, a pencil and paper puzzle in the manner of Sudoku.

The Grabarchuk Family
The Grabarchuk Family Photograph: The Grabarchuk family

If you enjoyed today’s puzzles please consider donating to Ukraine. Here are links to the National Bank of Ukraine’s donation pages for humanitarian and military support.

The Grabarchuks are on Facebook, Instagram, and here’s their website. Their most recent books are the Age of Puzzles series. All images in this story are their copyright.

I set a puzzle here every two weeks on a Monday. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.

I’m the author of several books of puzzles, most recently the Language Lover’s Puzzle Book. I also give school talks about maths and puzzles (online and in person). If your school is interested please get in touch.

On Thursday 21 April I’ll be giving a puzzles workshop for Guardian Masterclasses. You can sign up here.

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