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4Methyl-5,6,7,8-tetrahydroquinoline | C10H13N | CID 185667 - structure, chemical names, physical and chemical properties, classification, patents, literature

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Évangileselon Jean 5:2-8 La Bible en Français Courant (FRC97). 2 Dans cette ville, il y a, près de la porte des Brebis, une piscine avec cinq galeries à co

Earlier today I set you the following puzzles. Fill in the blanks so that these equations make arithmetical sense10 9 8 7 6 5 4 3 2 1 = 2016, and4 4 4 4 4 = 2016The solutionsFirst I’d like to say THANK YOU to the hundreds of people who left solutions at the bottom of the question post, on the Guardian Facebook page, on Twitter with the hashtag MondayPuzzle and in emails to been totally overwhelmed by the quantity and variety of solutions - and quite embarrassed that my own was so boring!Evidently there is no unique solution - I was half hoping a computer scientist would let me know exactly how many solutions there are with only the four basic operations. Maybe someone will...Before we get to my favourites, I’ll explain how I did it myself. Since a fair amount of you were way to solve this type of puzzle is through “enlightened” trial and error. My approach always begins by factorising the year, in this case 2016. Factorising means dividing in to smaller and smaller pieces so that all is left is a string of prime breaks down into 2 x 2 x 2 x 2 x 2 x 3 x 3 x 7, which is the same as 25 x 32 x 7When I saw this I thought that I would leave 7 as it is, and then try to make 25 and 32 32 and 9 out of 10 9 8 and 6 5 4 3 2 1.If this worked I’d have 10 9 8 x 7 x 6 5 4 3 2 1 = 2016I quickly noticed that 10 – 9 + 8 = 9. And then playing around that6x5 - 4 + 3 + 2 + 1 = I had a solution 10 – 9 + 8 x 7 x 6x5 – 4 + 3 + 2 + 1 = 2016It is a pretty dull solution though. The most elegant has to be this one, tweeted earlier by James Annan and subsequently by others10 x 9 x 8 x 7 x 6/5 + 4 + 3 + 2 + 1 = 2016I also found this one very cleanAnd this one also asked for you to come up with your most creative solutions using different mathematical operations. I found Adam’s particularly innovative, since he managed to use modular arithmetic and base 5 logarithms! But log5 24 = so his expression is only equal to Nice try...I award my runner up prize to Muhammad Khairy, for his marvellous solution with seven factorials and five square a few extra exclamation marks!!!But my favourite is this one since it uses square roots, powers, modular arithmetic mod 7776 for heaven’s sake, factorials and even trigonometry. Well done Sebastian! I’ll send you a copy of my book.alexbellos Hehe, I made an account just to post this ridiculous thing [10*sqrt9*8! / 7 modulo 6^5] + 4!*3!*2! + arccos1— Sebastian Radu magicsebi January 4, 2016 There may have been other good ones but I ran out of time...Now the second solution is 4 + 4 44 – 4 = 2016This is how I solved itAs someone who thinks about numbers quite a lot I looked at 2016 and it reminded me of 2048, which is one of the powers of two. If you start with two, and double it repeatedly you will soon get to = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 211I also realised that if you are going to multiply five fours together, you only get 10244 x 4 x 4 x 4 x 4 = 1024So the solution was probably going to feature 44 = 256Now lets return to 2016, the number we want to get we half it we get 1008, and if we half it again we get 504, and if we half it again we get ON!!!This number is 256 – is 44 – 44 – 4 = 2016/8 Multiplying by 8 8 x 44 – 4 = 20164 + 4 44 – 4 = 2016Thanks again for taking part. It has been an extremely fun day. I’ll be back with another puzzle in two post a puzzle here on a Monday every two most recent book is the mathematical adult colouring book Snowflake Seashell Star. In the US its title is Patterns of the Universe.You can check me out on Twitter, Facebook, Google+ and my personal if know of any great puzzles that you would like me to set here, get in touch. BdpV. 77 80 194 358 266 382 397 30 152