If you like number patterns, here’s something to look forward to next year.
Shortly after 10pm on February 22, the time and date will consist of a single repeating digit – the last time it will happen this century.
22:22:22/22/2/22
Toot toot!
Which leads us to today’s first puzzle.
1. What was the question?
The person at the rail station’s information desk replied: “2222222”
What was the question?
2. The question I ask every year – with the smallest incremental change.
This is an annual ritual for the readers of this column. Fill in the gaps so the following equation makes sense:
10 9 8 7 6 5 4 3 2 1 0 = 2022
You are allowed to use the mathematical symbols +, -, x, ÷ and as many brackets as you like. In other words, your answer should be of the form , 10 x 9 + (8 – 6) x 5 x 4 – ((3 x 2) + 1)), although not this one, which doesn’t equal 2022.
3. Three twos and a nought.
Construct the numbers from 1 to 10 with the digits 2, 0, 2 and 2. You are allowed to used the mathematical symbols +, -, x, ÷, √, the decimal point, the factorial !, as many brackets as you like, concatenation and exponentiation. You are also allowed to use the symbol for repeating decimals, usually a dot or a bar on the digit that is to be repeated ad infinitum.
For example, an expression for 7 is:
(.2/.02) – 2
There isn’t a way to draw a dot or a bar on a digit using this software, so I have denoted a repeating digit by having it in bold. .02 is thus .02222… where the 2s go on for ever.
Clarifications: The factorial symbol ! means that the following whole number is multiplied by each of the whole numbers less than it. For example, 3! = 3 x 2 x 1. Concatenation means you can place two or more digits together, as in .02 above, and exponentiation means you can have numbers a and b in the form ab.
NO SPOILERS PLEASE I’ll be back at 5pm UK with the solutions. Meanwhile, please post your favourite facts about 2022 below.
UPDATE: You can read the solutions here.
Thanks to Inder Taneja for reminding me of the monodigital date. Inder is an international guru of number patterns, and has written a 78-page article about all the fun and games to be had with 2022. My favourite is the following: both expressions add to 2022 when read normally, when read upside down, and when read in a mirror.
Thanks also to Lewis Baxter for suggesting the third puzzle. In fact, Lewis extended the brief and has worked out all possible fractions (with single digit numerators and denominators), using only the digits 2,0,2 and 2 and the operations listed above. He has found expressions for all of them except 8/7. If anyone can find an expression for 8/7, let us know!
Finally, thanks to all the readers of this column; this year it received almost 3 million views. Please keep on suggesting puzzles, making recommendations, improving on my answers and spotting mistakes. In case you missed them, the five most popular puzzles were:
1. Oxford university admissions questions
2. The magic of the Borromean rings
4. Russia’s Prime Minister sets a geometry puzzle
Happy New Year!
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.
