Commander Posted June 13, 2017 Share Posted June 13, 2017 Find the Master Magic Squares of 9x9 Magic Squares using Numbers from 1-81 This is a CASCADED VERSION with LOOSE ONION PEELS DESIGN in that : The Middle Core 3x3 Square is a Magic Square using 9 numbers from 1-81 This is enveloped by a 5x5 Magic Square using 16 more numbers in addition to the 9 numbers already used in the core 3x3 MS thus using a total of 25 numbers out of 1-81 This 5x5 MS is further enveloped by a 7x7 Magic Square adding another 24 numbers thus using a total of 49 numbers out of 1-81 Finally this 7x7 MS is enveloped by a 9x9 Overall Magic Square using all numbers 1-81 To illustrate please see the figure : This illustrates how each colored Core forms a 3x3 5x5 7x7 & 9x9 Magic Square respectively ! It can also be seen that each of these Magic Squares as well as these Sleeves can be rotated & still have a Magic Square & therefore there are many Solutions Possible To Illustrate further I give a Sample 9x9 1-81 Magic Square and analyze for illustration how it will add up in the smaller Squares within We can see here a 9x9 Sample Magic Square and to help add the Columns Rows & Diagonals I have indicated their Totals too. We can see that the Overall MS adds to the Magic Sum of 369 correctly where us the Component 3x3 5x5 & 7x7 Squares are not Magic Squares The Solution to the Puzzle requires all of these Components to be Magic Squares with Most likely Magic Sums of 123, 205,287 & 369 respectively ! There could be many Solutions Puzzle 1 : Find a Solution with 1-81 numbers so arranged that we have 3x3 5x5 7x7 & 9x9 Magic Squares cascaded like illustrated Puzzle 2 : Find a Solution with 1-81 numbers so arranged that we have 3x3 5x5 7x7 & 9x9 Magic Squares cascaded like illustrated with each Magic Square having Sequential numbers. Like 3x3 MS with numbers 1-9 or 37 - 45 etc followed by 5x5 MS with 1-25 or 29-53 and so on. Like in the above sample 9x9 MS has sequential numbers from 1-81 Similarly the component 3x3 5x5 & 7x7 each must have a sequential Block of numbers out of 1-81 3x3 MS need not start with 1 [perhaps can not] Link to comment Share on other sites More sharing options...
Commander Posted June 16, 2017 Author Share Posted June 16, 2017 Has anyone attempted this ? 1 Link to comment Share on other sites More sharing options...
Commander Posted June 19, 2017 Author Share Posted June 19, 2017 Can our Puzzle Solvers pay some attention to Magic Squares ! Link to comment Share on other sites More sharing options...
Commander Posted June 26, 2017 Author Share Posted June 26, 2017 I am placing this on Twitter & Facebook too ! Be the FIRST in the UNIVERSE to Solve it ! Link to comment Share on other sites More sharing options...
Commander Posted August 23, 2017 Author Share Posted August 23, 2017 Hello All ! Now that sufficient time has passed can I give the Solutions ? Link to comment Share on other sites More sharing options...
Commander Posted March 27, 2018 Author Share Posted March 27, 2018 Please tell me if everyone has given up after trying ! Should we have the Solution given here ? Link to comment Share on other sites More sharing options...
Commander Posted March 27, 2018 Author Share Posted March 27, 2018 We have discussed various MAGIC SQUARES in many Puzzles posted here. I summarize here some of the Solutions/Derivations we have SOLVED so far. A 9x9 Magic Square with Mini 3x3 Squares having Diagonals add to 123 Best Solution for a 9x9 Magic Square with each 3x3 Cell adding as close to 123 [not possible for every cell to add up to 123] Sample of Random order & Sequential Order And FINALLY we give here the Solution to the First Puzzle with Random distribution of numbers 1-81 but making the required Core Onion Shells What is NOW LEFT is to find that Solution which will have a Sequential Solution that is : Each of the Core 3x3 , 5x5 , 7x7 & 9x9 Magic Square will be of a Continuous Block of Numbers from 1-81 That is 3x3 MS will have from 37-45, 5x5 MS from 29-53 etc. NOW THERE IS NO EXCUSE NOT TO FIND THE SOLUTION ! Goodluck ! Link to comment Share on other sites More sharing options...
Amit Walker Posted May 1, 2018 Share Posted May 1, 2018 Solved dad!! See the solution given below 1 Link to comment Share on other sites More sharing options...
Commander Posted May 1, 2018 Author Share Posted May 1, 2018 (edited) 35 minutes ago, Amit Walker said: Solved dad!! See the solution given below Well done Amit ! I have put your solution into the format as below There may be many Solutions & I give below the Solution found by me ! Congratulations for finding the Solution ! Edited May 1, 2018 by Commander Link to comment Share on other sites More sharing options...
Amit Walker Posted May 1, 2018 Share Posted May 1, 2018 Link to comment Share on other sites More sharing options...
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