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Can you solve it? 2019 in numbers

To welcome the New Year, we’re going to celebrate the number 2019. Here’s one numerical factoid readers may find charming:

Ed Southall
(@solvemymaths)

2019 is the smallest number that can be written in 6 ways as the sum of the squares of 3 primes:

7² + 11² + 43² = 2019

7² + 17² + 41² = 2019

13² + 13² + 41² = 2019

11² + 23² + 37² = 2019

17² + 19² + 37² = 2019

23² + 23² + 31² = 2019

December 30, 2018

Thanks Ed! Please add your pleasing 2019 number patterns in the comments below. Meanwhile, today’s puzzles:

1) Date jam

(i) Using only the digits 2, 0, 1 and 9, create expressions that equal all of the numbers from 0 to 12. The expressions can include any of the arithmetical symbols +, –, x, ÷ and √, and brackets.

I’ll start you off:

  • 0 x (2 + 1 + 9) = 0

  • 2 – 1 + (0 x 9) = 1

Note: you must use each of the digits 2, 0, 1 and 9 once and only once in each expression.

(ii) Create expressions using 2, 0, 1 and 9 for all the numbers from 13 to 20. Again each number must be used once and only once in each expression, but as well as the operators mentioned above you can now use concatenation (meaning you can join numbers up, for example, a 2 and a 0 can concatenate to 20) and exponentiation (meaning that one number can be the power of another, such as 19).

(iii) How much higher can you go with just 2,0, 1 and 9? What other mathematical symbols do you need to create expressions all the way to 100?

2) Countdown conundrum

Fill the blanks in the following equation, so that it makes arithmetical sense:

10 9 8 7 6 5 4 3 2 1 = 2019

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) = 2019, but not this one since the equation is incorrect.

There are many solutions. I’ll give a copy of my puzzle book Puzzle Ninja to the one I like the best. You can either tweet me or email me your solutions.

The countdown conundrum is an annual tradition in this column. With some trial and error you will hopefully find a solution. What better way to end 2018 with a sense that you have already conquered 2019! Happy New Year everyone!

I’ll be back at 5pm UK time today with solutions.

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.


Photograph: Walker Books

I’m the author of several books of popular maths, and the Football School book series for kids that explains the world through football. The Football School Collection is out now.