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]

Has anyone attempted this ?

Can our Puzzle Solvers pay some attention to Magic Squares !

I am placing this on Twitter & Facebook too !

 

Be the FIRST in the UNIVERSE to Solve it !

Hello All !

Now that sufficient time has passed can I give the Solutions ?

 

Please tell me if everyone has given up after trying !

Should we have the Solution given here ?

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 !

Solved dad!!

See the solution given below 

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, 20187 yr by Commander