Earlier today I set the following three puzzles, variations on the same theme:
Fill in the equations below using any of the basic mathematical operations, +, –, x, ÷, and as many brackets as you like, so that they make arithmetical sense.
1) 10 9 8 7 6 5 4 3 2 1 = 2017
2) 9 8 7 6 5 4 3 2 1 = 2017
3) 8 7 6 5 4 3 2 1 = 2017
The pleasure of these puzzles is in the elegance of the statement, the simplicity of the tools required and the achievability of a solution. As I wrote, there are almost a thousand ways to solve the first one.
I usually solve these problems by dividing the year into its divisors, and then trying to make each divisor from the ten digits. This method was not possible this year since 2017 is prime. So what I did - and I think many of you did too - was to find an expression that ended in either + 1 or + 2 – 1, and make the numbers from 10 to 2, or 10 to 3, equal the much friendlier 2016.
I received dozens of different solutions to the first question, the ten-countdown. The most popular one was also to my mind the most appealing, since you can write it without brackets, assuming you perform the operations in order from left to right. The first person to enter this was the Tweeter A Bernery. A copy of my book on its way to you, sir! (Or madam, hard to say from the image).
Solved it, or came up with 1 solution anyhow:
— A. Bernery #NoDAPL (@_Anunnery) January 2, 2017
Operations in order, no brackets:
10 * 9 * 8 * 7 / 6 / 5 * 4 * 3 + 2 - 1 = 2017 #MondayPuzzle https://t.co/hL6lq5J5Up
The most concise solution for the the nine-countdown was sent in via email from Dima:
9 x 8 x 7 x (6 – 5) x 4 x (3 - 2) + 1 = 2017
And my preferred solution to the third one was in a comment to my original post by LadyLoverlysChatter and uses similar thinking:
8 x 7 x 6 x (5 - 4) x 3 x 2 + 1 = 2017
The bonus question in the photo caption, to find numbers for H, E, L and O such that H E L L O = 2017 was not solved by anyone!
If H = 7, E = 8, L = 6 and O = 1, then H x E x L x L + O = 2017
Thanks for getting involved and I’ll see you in two weeks for some more Ja-neuron-ary puzzle action.
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.
My new book Can You Solve My Problems? A Casebook of Ingenious, Perplexing and Totally Satisfying Puzzles is available from the Guardian Bookshop and other retailers. My children’s book Football School: Where Football Explains The World was recently shortlisted for the Blue Peter Book Award 2017.
