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Subtraction and Division with 3 or more squares https://www.calcudoku.org/forum/viewtopic.php?f=2&t=4 
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Author:  larryb33 [ Sat May 14, 2011 4:59 pm ] 
Post subject:  Subtraction and Division with 3 or more squares 
Before discovering the puzzles on this site, I had only seen the  and / operators with 2 squares. I had assumed this would be the case since multiplication and addition are associative operations whereas subtraction and division are not. Has anyone else felt confusion over the quotient of 4,8,2 for example? I see a potential ambiguity with (8/4)/2 = 1, 8/(4/2) = 4, 4/(2/8) = 16, etc. Anyway, after solving many of these puzzles, it seems that the convention is to always subtract and divide in descending order. Is this correct? 
Author:  sneaklyfox [ Sat May 14, 2011 5:15 pm ] 
Post subject:  Re: Subtraction and Division with 3 or more squares 
Dividing or subtracting in descending order is mostly correct although it can be either 8/4/2 or 8/2/4. The highest number goes in the front. Or really, it can be any order but without using brackets. The highest number must be the first one if you want a nonfractional or nonnegative result. 
Author:  larryb33 [ Sat May 14, 2011 6:23 pm ] 
Post subject:  Re: Subtraction and Division with 3 or more squares 
That make sense, thanks. I suppose I can't go wrong with highest number minus the sum of the others and highest number divided by the product of the others. 
Author:  richr [ Tue May 17, 2011 7:16 pm ] 
Post subject:  Re: Subtraction and Division with 3 or more squares 
Any order is OK as long as the result is a non negative integer. Sometimes a different order gives different results, like 9,3,3: (= either 9 or 1) . As long as one of the results fits, it is OK. 
Author:  maartensmit [ Tue May 17, 2011 7:20 pm ] 
Post subject:  Re: Subtraction and Division with 3 or more squares 
richr wrote: Any order is OK as long as the result is a non negative integer. Sometimes a different order gives different results, like 9,3,3: (= either 9 or 1) . As long as one of the results fits, it is OK. That's not true. 9 3 3 only yields 1 as answer, not 9 (I think you meant 9/(3/3) = 1?) The best way to solve this problem is as sneaklyfox already said, to not use brackets and always put the numbers in descending order. 
Author:  larryb33 [ Tue May 17, 2011 9:49 pm ] 
Post subject:  Re: Subtraction and Division with 3 or more squares 
maartensmit wrote: The best way to solve this problem is as sneaklyfox already said, to not use brackets and always put the numbers in descending order. I just thought of an exception to descending order with division, but only when 0 is possible. If 3 squares are labeled 0/, you know the order of division will be 0/x/y (obviously not descending). 
Author:  maartensmit [ Tue May 17, 2011 9:53 pm ] 
Post subject:  Re: Subtraction and Division with 3 or more squares 
larryb33 wrote: maartensmit wrote: The best way to solve this problem is as sneaklyfox already said, to not use brackets and always put the numbers in descending order. I just thought of an exception to descending order with division, but only when 0 is possible. If 3 squares are labeled 0/, you know the order of division will be 0/x/y (obviously not descending). Ah, yes, that is true. I didn't think of that, I always skip the puzzles with zero 
Author:  sneaklyfox [ Wed May 18, 2011 1:45 am ] 
Post subject:  Re: Subtraction and Division with 3 or more squares 
maartensmit wrote: 9 3 3 only yields 1 as answer, not 9 (I think you meant 9/(3/3) = 1?) 9/(3/3) = 9/1 = 9 But anyway, the puzzles don't work like that. No brackets. As for the zero puzzles, you have to forget that there is such a thing as x/0 = infinity because the puzzles do allow you to have more than one zero in a 0: box (in L configuration, for example). Assuming that none of the puzzles operate with brackets, that should not be possible. So you can treat 0/0 = 0. 
Author:  pnm [ Thu May 19, 2011 11:28 am ] 
Post subject:  Re: Subtraction and Division with 3 or more squares 
sneaklyfox wrote: 9/(3/3) = 9/1 = 9 But anyway, the puzzles don't work like that. No brackets. As for the zero puzzles, you have to forget that there is such a thing as x/0 = infinity because the puzzles do allow you to have more than one zero in a 0: box (in L configuration, for example). Assuming that none of the puzzles operate with brackets, that should not be possible. So you can treat 0/0 = 0. Spot on in both cases. No brackets are involved, and you can't do division by zero (so a cage with 3 cells can never have 2 zeroes, for example) Patrick 
Author:  sneaklyfox [ Fri May 20, 2011 2:57 am ] 
Post subject:  Re: Subtraction and Division with 3 or more squares 
Can't have two or more zeros in a cage? Ok, maybe I forgot. I just thought maybe that had happened. Maybe it was 0x. 
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