Complete the countdown conundrum 10 9 8 7 6 5 4 3 2 1 = 2017 and win a prize
Here in Numberland, we always knew that 2016 was going to be a bad one, since:
2016 = 666 + 666 + 666 + 6 + 6 + 6
But thats last years news. Whats the story about 2017, arithmetically speaking?
Well, 2017 is a prime number – the first since 2011, and the last until 2027. (Prime numbers are those numbers that are only divisible by themselves and 1.)
More notably, 2017 is the smallest whole number whose cube root begins with ten distinct digits:
20171/3 = 12.63480759….
Wowza! At this time of year, many mathematically curious folk spend time looking for satisfying number patterns like this one involving the new date. (Please add your favourites in the comments below.)
Just so you are not left out the fun, todays puzzle is to fill the blanks in the following equation, so that it makes arithmetical sense:
10 9 8 7 6 5 4 3 2 1 = 2017
You can use any of the basic mathematical operations, +, , x, , and as many brackets as you like. So, an answer might look something like (10 + 9 + 8) x (7 6 5)/(4 + 3 + 2 + 1) = 2017, although not this one since this is incorrect.
I do this countdown equation every year. Because 2017 is prime, it is a little bit more difficult that last years equation where the numbers had to equal 2016. In fact, there are only 652 solutions this year, compared with 890 solutions for last year, according to my computer programmer pal Zefram. (Many of these solutions are similar).
Got that? Now lets raise the stakes. Can you do the same to this equation, which is the same as above but with the 10 deleted:
9 8 7 6 5 4 3 2 1 = 2017
There are only 107 solutions to this one.
Now you have a taste for this puzzle, fill in the equation with the 9 deleted too:
8 7 6 5 4 3 2 1 = 2017.
This one only has 13 solutions. Its interesting that each time we remove a number the solution space shrinks by a factor of about seven.
We have to end there, since there are no solutions when only seven digits are left.
I stipulated above that you must use only the four basic mathematical operations. But of course, if you want to show off, you can use whatever arcane or complicated mathematical operations you want.
I will send a copy of my puzzle book Can You Solve My Problems? to the person who comes up with the solution to any of the three above puzzles that I consider to be the most beautiful, creative or wacky. This could be one with, say, the least number of brackets required, or with the most ambitious use of mathematical symbology. My decision is final!
To enter either tweet your answer with the hashtag #MondayPuzzle or email me. Ill be back with answers and results at the end of the day.