4 x 4 cards

[BMAD]

Take from a pack of cards all the Aces, Kings, Queens and Jacks.

Arrange them in a 4 × 4 square so that every row, column and diagonal contains one card of each value (A,J,Q,K) and one card of each suit (Heart, Spade, Diamond, Club).

[BMAD]

nice. now how many different 'correct' answers are there?

  On 3/8/2013 at 2:20 PM, dark_magician_92 said:

  Reveal hidden contents

HA SK DJ CQ

CJ DQ SA HK
SQ HJ CK DA
DK CA HQ SJ

  On 3/8/2013 at 7:58 AM, bhramarraj said:

  On 3/8/2013 at 7:52 AM, bhramarraj said:

  Reveal hidden contents

AS QC JH KD

JD KS AC QH

KC JS QD AH

QH AD KS JC

IN SECOND ROW SECOND COLUMN IT SHOULD BE 'KH'. I TRIED TO EDIT THE POST BUT EDITING FAILED.

  On 3/8/2013 at 5:56 AM, bonanova said:

  Reveal hidden contents

As Kh Qd Jc

Jd Qc Ks Ah

Kc Ad Jh Qs

Qh Js Ac Kd

[vistaptb]

  Reveal hidden contents

SA HK DQ CJ

CK DA HJ SQ
DJ CQ SK HA
HQ SJ CA DK

(H=hearts, S=spades, D=diamonds, C=clubs, A=ace, Q=queen, K=king, J=jack)

[BMAD]

  On 3/8/2013 at 3:43 AM, vistaptb said:

  Reveal hidden contents

SA HK DQ CJ

CK DA HJ SQ

DJ CQ SK HA

HQ SJ CA DK

(H=hearts, S=spades, D=diamonds, C=clubs, A=ace, Q=queen, K=king, J=jack)

  Reveal hidden contents

your diagonals don't meet the requirement of the op

Edited March 8, 2013 by BMAD

[bonanova]

  Reveal hidden contents

As Kh Qd Jc

Jd Qc Ks Ah

Kc Ad Jh Qs

Qh Js Ac Kd

[bhramarraj]

  Reveal hidden contents

AS QC JH KD

JD KS AC QH

KC JS QD AH

QH AD KS JC

Edited March 8, 2013 by bhramarraj

[bhramarraj]

  On 3/8/2013 at 7:52 AM, bhramarraj said:

  Reveal hidden contents

AS QC JH KD

JD KS AC QH

KC JS QD AH

QH AD KS JC

IN SECOND ROW SECOND COLUMN IT SHOULD BE 'KH'. I TRIED TO EDIT THE POST BUT EDITING FAILED.

[bonanova]

  On 3/8/2013 at 7:58 AM, bhramarraj said:

  On 3/8/2013 at 7:52 AM, bhramarraj said:

  Reveal hidden contents

AS QC JH KD

JD KS AC QH

KC JS QD AH

QH AD KS JC

IN SECOND ROW SECOND COLUMN IT SHOULD BE 'KH'. I TRIED TO EDIT THE POST BUT EDITING FAILED.

Hint: To edit after time elapses, copy / edit / paste onto a new post.

[dark_magician_92]

  Reveal hidden contents

HA SK DJ CQ

CJ DQ SA HK
SQ HJ CK DA
DK CA HQ SJ

[bonanova]

  On 3/8/2013 at 5:33 PM, BMAD said:

nice. now how many different 'correct' answers are there?

Excluding rotations and mirror images,

  Reveal hidden contents

There is only one solution.

Without loss of generality, we can fill in the top row with choices.

Eliminating duplicates in rows, columns and diagonals we have

We see that the center and corner squares have only two possibilities.

Choosing each leads to two solutions:

........

Note the patterns of the a cells are diagonal mirror images.

Call the patterns CW and CCW respectively.

In the CCW case the c cells include the opposite corner cell.

They have a CCW pattern as well.

Together they look like this.

.

Now it is clear that the remaining cells can be filled in with CW patterns for b and d.

So this is the basic pattern for isolating four entities in a 4x4 grid.

It would apply to card rank or card suit equally well.

To isolate two sets of four entities, one would simply overlay one

of the above choices for Rank with the other choice for Suit.

That is the construction for the single solution to this puzzle.

It has only reflection and rotation variants.

[18 IXOHOXI 81]

There are 144 distinct solutions times 8 rotations and reflections for a total of 1152 solutions for the 4x4 Magic Court Card Puzzle. Solution # 1: AS KH QD JC QC JD AH KS JH QS KC AD KD AC JS QH. Solutions # 2: AS KH QD JC JD QC KS AH KC AD JH QS QH JS AC KD. Plus there's 1150 more solutions that satisfies the conditions that each of the four card ranks and four card suits appears only once in each of the four rows, four columns, and the two diagonals. This also works if the cards came from a four color deck.