Alex Bellos's Adventures in NumberlandMathematics

New year conundrum: complete the equation 10 9 8 7 6 5 4 3 2 1 0 = 2014

This annual numerical challenge will delight recreational mathematicians with time on their hands

In the runup to the end of December, the Guardian has published countdowns of TV shows, films and football players.

So here's one with numbers. The challenge is to count down from 10 to 0, and to fill in the gaps so that the expression equals the year.

In other words, fill in the gaps so the following equation makes sense:

10 9 8 7 6 5 4 3 2 1 0 = 2014

The conundrum is a seasonal variant on a charming and traditional arithmetical game, the "four fours", which dates back at least to Victorian times. You have four fours:

4 4 4 4

Using only the four basic maths symbols, which are +, –, x, ÷, (plus, minus, times, divide), the aim is to use all four fours to create an expression for each digit from 0 to 9. (Brackets are also allowed, to make it clear which operations need to be done first)

Let's start:

4 – 4 + 4 – 4 = 0

(4 + 4)/(4 + 4) = 8/8 = 1

(4 x 4)/(4 + 4) = 16/8 = 2

Now continue all the way up to 9. If you have never attempted to do this before, it's a great diversion when on trains and planes, which might be the case if you are travelling over the new year period.

If that was fun, then once you start to allow concatenation – ie you can put the fours together to get a 44 – and introduce other symbols such as the square root √, the factorial ! and the decimal point ., it is possible to make the four fours equal every number up to 100. Remember you are only allowed four 4s and you have to use all of them.

Now back to the countdown challenge. I first became aware of it last year when I saw:

(10 + 9 – 8)(7 - 6 + (5)(4)(3))(2 + 1 + 0) = 2013

Beautiful!

Here's one for the new year, devised by my friend Bob Wainwright at Iona College, near New York.

(10+9)((8)(7)+6-5-4)(3-2+1+0) = 2014

There are more solutions, using only the four basic arithmetical operations and also using the more advanced ones. Can you find them? (Tip: Start by factorising the number, and see where it leads you … ) If no one has posted them below by 1 January, I'll add them in the comments section.

ncG1vNJzZmivp6x7tbTEoKyaqpSerq96wqikaKuTnrKvr8RomKWdqKh6orDVnqWtraKawG61zWalrqWSmr%2Btrc2dZmtoYWh8pbHCaGppZ56axG7FxJqpZpufqru1sM6wpWadoaqutbXOp2SmmaSdsq6t06KarA%3D%3D