Hello all,I"d favor to re-publishing a puzzle, a partial solution, and a inquiry for some an ext help (or comments).The puzzle is native an old maths textbook pitched at 12-14 year olds, yet has potential for development into more difficult territory.Quote: "Creating Numbers: a task requiring imagination Your job is to develop every number indigenous 1 to 50. You deserve to use just the numbers 1, 2, 3 and also 4 as soon as in each and the work + - x / . You can use the numbers as powers, and also you need to use all of the numbers 1, 2, 3, 4. Here are some examples: 1 = (4-3) / (2-1)20 = 42 +3 +168 = 34 x 2 x175 = (4+1)2 x 3End Quote.I"ve controlled the job of generating all the numbers from 1 to 50, and having excellent that, I"ve started relocating on to 51-60 and also possibly further.My full work for this reason far, and the gaps I"ve encountered between 51 and 60 are here:http://davechessgames.blogspot.com/2015/06/numbers-from-1234-to-50.html have the right to anybody assist me with my gaps? Or - conversely - prove that the gaps can"t be completed?ThanksDavid

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Thanks, Denis - for the suggestions, comments, and additional solutions for 57.I have actually made the correction girlfriend highlighted, and adjusted all the x come * many thanks for recall me top top the correct symbol to usage online
I"ll keep number-crunching and also see what else I have the right to get.Kind regardsDavid

ThanksThanks, Denis, for her reply.I"m not certain why factorial wasn"t permitted in the original rules - maybe the textbook writer didn"t think your target audience would certainly know about factorials. In any case, I"ve made decision that we need factorials - and decimals - to continue the game! thanks for your services for 57, and the correction come 28 - ns have included these to the blog, and also I"ve also readjusted the multiplication symbol indigenous x come * many thanks for remind me of correct notation.I"ll keep number-crunching and also see if there room any much more gaps I deserve to fill in v decimals and factorials!Kind regardsDavid
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DavidLeese,here room some expressions because that the remaining numbers:53 = (1 + 4!)2 + 353 = (3 + 4!)2 - 156 = (1 + 4!)2 + 3! 56 = (1 + 3 + 4!)256 = 41 + 3/.256 = 4! + 3/.1 + 2