Problem 1697. Make a Pandiagonal Prime Magic Square: 11 x 11

Created by Richard Zapor

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This Fun with Primes Challenge is to create a Pandiagonal Prime Magic Square of size 11x11 given eleven APk sequences with 10 constant offsets and 121 unique prime values.An APk sequence is of the form P + offset(i) where P is a prime and i=1:11 with offset(1)=0 and offset(j)>offset(i), j>i.A Pandiagonal Magic Square has all rows, columns, diagonals(including broken), and anti-diagonals(including broken) summing to the same value.Input: APk matrix (11,11)Output: Pandiagonal Matrix (11,11)Algorithm:The 11x11 algorithm can be summarized as circular shift of rows to make all columns sum to the same goal value. The goal value is the diagonal sum of the APk matrix. Use Knight moves +2 rows +1 column, with bottom to top wrap.<pre class="language-matlab">Detailed Methodolgy:
1) PS : Shift APk rows 2 thru 11 by 2*(row value)
2) First column of PS will be first column of P
3) P from PS row 1 : P(1,1)=PS(1,1), P(3,2)=PS(1,2) or P(delta Knight)=PS(row,next). The P(3,2) is 2 down and 1 over from P(1,1).
4) Repeat Knight moves starting at P(row,1) for the remaining rows.
</pre>Related Challenges:1) <a href = "http://www.mathworks.com/matlabcentral/cody/problems/1673-pandiagonal-prime-magic-square-verification">Pandiagonal Check</a>2) Find 11x11 Pandiagonal 18191 APk setRestrictions: No str2num or regexp (enforced as necessary)

This Fun with Primes Challenge is to create a Pandiagonal Prime Magic Square of size 11x11 given eleven APk sequences with 10 constant offsets and 121 unique prime values.

An APk sequence is of the form P + offset(i) where P is a prime and i=1:11 with offset(1)=0 and offset(j)>offset(i), j>i.

A Pandiagonal Magic Square has all rows, columns, diagonals(including broken), and anti-diagonals(including broken) summing to the same value.

*Input:* APk matrix (11,11)

*Output:* Pandiagonal Matrix (11,11)

*Algorithm:*

The 11x11 algorithm can be summarized as circular shift of rows to make all columns sum to the same goal value.  The goal value is the diagonal sum of the APk matrix. Use Knight moves +2 rows +1 column, with bottom to top wrap.

Detailed Methodolgy:
  1) PS : Shift APk rows 2 thru 11 by 2*(row value)
  2) First column of PS will be first column of P
  3) P from PS row 1 : P(1,1)=PS(1,1), P(3,2)=PS(1,2) or P(delta Knight)=PS(row,next). The P(3,2) is 2 down and 1 over from P(1,1).
  4) Repeat Knight moves starting at P(row,1) for the remaining rows.

*Related Challenges:*

1) <http://www.mathworks.com/matlabcentral/cody/problems/1673-pandiagonal-prime-magic-square-verification Pandiagonal Check>

2) Find 11x11 Pandiagonal 18191 APk set

*Restrictions: No str2num or regexp (enforced as necessary)*

Solve

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Last Solution submitted on Mar 12, 2023

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James on 9 Jul 2013

Richard, I think your test suite has an error in it. Both pd and pad will result in the same matrix, as they're both circshifted by [1 1-i] Will pad=fliplr(pad); after the for loop correct this problem?

Richard Zapor on 9 Jul 2013

Test Suite fixed. Who new that 1-i is the same as -i+1.

Rafael S.T. Vieira on 18 Aug 2020

The circular shift should be made from first row, not the 2nd, and the "knight" always moves down from the first column of the row to the last column in an L-movement.

Marco Riani on 21 Jan 2022

I fully agree with the comments by Rafael S.T. Vieira. The problem is nice but it was badly explained

Solution Comments

Solution 276720

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Richard Zapor on 9 Jul 2013

I had not recognized the symmetry of row and column processing. A very succinct method to create a Knight pattern.

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Problem 1697. Make a Pandiagonal Prime Magic Square: 11 x 11

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Problem 1697. Make a Pandiagonal Prime Magic Square: 11 x 11

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