Count von Count will be fizzing with excitement. For the first time since 1920, the coming year, 2021, consists of two ascending, consecutive numbers. Enjoy this ‘counting date’ while it lasts, people! It ain’t going to happen again for another hundred and one years.

Today’s puzzles reveal more arithmetical patterns concerning 2021.

**1. Countdown conundrum**

The first question is an annual ritual. Fill in the blanks in the following equation so it makes arithmetical sense:

10 9 8 7 6 5 4 3 2 1 = 2021

You are allowed to use any of the basic mathematical operations, +, –, x, ÷, and as many brackets as you like. An answer might look something like (10 – 9 + 8) x (7 – 6 – 5)/(4 + 3 + 2 + 1) = 2021, but not this one since the equation is incorrect.

There are many correct answers – try to find the most elegant one.

**2. Inder’s enigmas**

Inder J Taneja, a retired maths professor from Brazil, likes to find ways to describe the new date using combinations of the same digit. For example, here’s how he does it with 1.

(1+1)^{11 }−(1+1+1)^{(1+1+1)} = 2021

Can you find combinations of 2’s, 3’s, 4’s 5’s, 6’s, 7s, 8’s and 9’s that also equal 2021? You are only allowed to use at most ten digits per equation. (Try at least one of them.) But you can concatenate, i.e, place two or more digits together in the same number, as above with 11.

**3. Marek’s mindbender**

The Polish puzzle creator Marek Penszko sent in the grid puzzle below, which you can print out here.

You must fill in each of the nine empty cells so that all the equations are correct. Each cell requires a single digit. Since 0, 1 and 2 are already visible, the only digits that can appear in the empty cells are the digits from 3 to 9, some of which appear more than once. The calculations are to be done strictly from left to right, or from top to bottom (ie. ignore operator precedence). [note: the ‘:’ is the symbol for division.]

I’ll be back at 5pm UK with a selection of my favourite 2021 equations and answers to the puzzles. Please fill the comments below the line with as many numerical curiosities about 2021 as you can!

UPDATE: the solutions and further discussion can be read here.

Finally, I’d like to wish the readers of this column a Happy New Year (in four days time) and say thank you for your continued support. The column totalled almost 3 million views in 2020. If you want to browse through the archive, the top five columns in order were:

1. Are you smart enough for MIT?

2. The bat, the ball and the bamboozle

3. The smallest, biggest triangle in the world

4. John Horton Conway, playful maths genius

*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.*

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