Next year is going to be something to look forward to if you like number patterns.
The last time a repeating digit was used in the time and date was after 10pm on February 22.
22:22:22
Toot toot!
Which leads us to the first puzzle.
1. What was the question?
The person at the information desk said, "2222222".
What was the question?
2. Every year, I ask the question with the smallest change.
This is a yearly ritual for the readers. The following equation can be made sense if you fill in the gaps.
10 9 8 7 6 5 4 2 1
You can use the symbols +, -, x, and as many brackets as you please. The answer should be of the form 10 x 9 + 8 x 6 x 5 x 4 + 1 which doesn't equal 2022.
3. Three twos and a zero.
The numbers from 1 to 10 are 2, 0, 2 and 2. You can use the mathematical symbols +, x,,, as many brackets as you want. You can use the symbol for repeating decimals, usually a dot or a bar on the digit that is to be repeated ad infinitum.
An expression for 7 is:
2
There isn't a way to draw a dot or bar on a digit using this software, so I have marked it with a repeating digit.
The factorial symbol means that the following whole number is less than the next one. 3 x 2 x 1. If you place two or more digits together, as in.02 above, you can have numbers a and b.
I will be back at 5pm UK with the solutions. You can post your favourite facts here.
I thank Inder Taneja for reminding me of the monodigital date. Inder, an international guru of number patterns, has written a 76-page article about all the fun and games to be had with 2022. When read upside down, and in a mirror, the expressions add to 2022.
Inder J. Taneja wrote a book called Mathematical Beauty of 2022, Zenodo.
Thanks to Lewis for suggesting the third puzzle. Lewis worked out all possible fractions using only the digits 2,0,2 and 2 and the operations listed above. He found expressions for all of them. Let us know if anyone can find an expression for 8/7.
Thanks to the readers of this column, this year it received almost 3 million views. I need to improve on my answers and suggest puzzles. If you missed them, the five most popular puzzles were:
1. admissions questions for Oxford
2. The Borromean has magic.
3. The crazy math of the coin.
4. Russia's Prime Minister sets a puzzle.
5. From Russia with logic.
Happy New Year!
I put a puzzle here on Mondays. I look for great puzzles. Email me if you would like to suggest one.
The Language Lovers Puzzle Book is the most recent book I have written. I give school talks about math and puzzles. Please contact your school if you are interested.
