Earlier today I set you the following three puzzles:

1. What was the question?

The person at the rail station’s information desk replied: “2222222”

What was the question?

Solution: “Can you tell me from when, and to when, the train will be in the station?”

The person at the information desk replied: “Two to 2:00, to 2:22.”

2. The question I ask every year – with the smallest incremental change.

In what 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.

Solution:

Here’s one solution. Please post others below.

10+(((9×8×7)−6+5)×(4+3−2−1))

3. Three twos and a naught.

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 factorial !, as many brackets as you like, concatenation and exponentiation. (It may be helpful to know that 0! = 1.)

1. 2220

2. 22 – 20

3. √((20-2)/2)

4. 2 + 2 – 02

5. 20/(2 + 2)

6. √((20 – 2) x 2)

7. (2 + 0!)2 – 2

8. (20/2) – 2

9. (20 – 2)/2

10. 20/√(2 x 2)

(In the original post I also said you could use the decimal point and the symbol for repeated decimal. In fact, it has subsequently been pointed out that you don’t need these operations at all. I think the solutions above are the simplest.)

Thanks everyone! I hope you enjoyed today’s puzzles. I’ll be back next year.

Thanks to Inder Taneja for help with today’s puzzles and solutions. You can read his 78-page article about all the fun and games to be had with 2022 here.

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.