bonanova Posted January 15, 2008 Report Share Posted January 15, 2008 Consider this 3x3 magic square, which sums horizontally, vertically and diagonally to 45: 5 22 18 28 15 2 12 8 25[/codebox] Find a way to convert it to another 3x3 magic square that sums to 21. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 15, 2008 Report Share Posted January 15, 2008 Do you mean to use a single mathmatical operator on all 9 numbers? Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 15, 2008 Report Share Posted January 15, 2008 Writersblock said: Do you mean to use a single mathmatical operator on all 9 numbers? Yup. bonanova said: which sums horizontally, vertically and diagonally to 45 Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 15, 2008 Report Share Posted January 15, 2008 Just to clarify, I didn't mean a single operator in solving the puzzle - that I knew. I refer to the means of conversion - does Quote Find a way to convert it mean you must do the same mathmatical "thing" to all 9 numbers and get them to "solve" to 21? Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted January 15, 2008 Author Report Share Posted January 15, 2008 Writersblock said: Just to clarify, I didn't mean a single operator in solving the puzzle - that I knew. I refer to the means of conversion - does mean you must do the same mathmatical "thing" to all 9 numbers and get them to "solve" to 21?Without commenting on the nature of what you do, do the same thing to each of the numbers to get a new srt of numbers. The new set of numbers, each in its respective place, forms a 21 magic square. Quote Link to comment Share on other sites More sharing options...
0 unreality Posted January 15, 2008 Report Share Posted January 15, 2008 Is it just me or was this very easy? Reveal hidden contents 5 22 18 28 15 2 12 8 25 subtract 8 from each number -3 14 10 20 7 -6 4 0 17 Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted January 16, 2008 Author Report Share Posted January 16, 2008 unreality said: Is it just me or was this very easy? Reveal hidden contents 28 15 2 12 8 255 22 18 subtract 8 from each number 20 7 -6 4 0 17-3 14 10 Well, [1] yes that works and [2] it is too easy. To be more responsive to Writersblock's question: What I have in mind is not mathematical. The numbers have a property that surprisingly creates a new magic square. That the new MS sums to 21 is just a piece of information that lets you verify that the MS you will have found is the one I had in mind. Have Fun ... ! Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted January 17, 2008 Author Report Share Posted January 17, 2008 Hint - the spoiler shows the new magic square. How was it constructed? Reveal hidden contents 11 7 3 6 5 104 9 8 Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 17, 2008 Report Share Posted January 17, 2008 bonanova said: Hint - the spoiler shows the new magic square. How was it constructed? Reveal hidden contents 4 9 8 11 7 3 6 5 10 It is just the number of letters in the original numbers. 5 has 4 letters etc. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 18, 2008 Report Share Posted January 18, 2008 Oddly enough you can also just start with the lowest # in the original square (the 2) make it a 3... then for each number in sequential order make it a 4, 5, 6, ... 2->3 5->4 8->5 ... 28->11 Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 23, 2008 Report Share Posted January 23, 2008 bonanova said: do the same thing to each of the numbers to get a new srt of numbers. Bit of a late entry but there is an even simpler solution. Do this 'mathematical thing' to each number: multiply by zero and add seven Quote Link to comment Share on other sites More sharing options...
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bonanova
Consider this 3x3 magic square, which sums horizontally, vertically and diagonally to 45:
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