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# 4 x 4 cards

## Question

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).

## Recommended Posts

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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)
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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)

your diagonals don't meet the requirement of the op

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As Kh Qd Jc

Jd Qc Ks Ah

Qh Js Ac Kd

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AS QC JH KD

JD KS AC QH

KC JS QD AH

Edited by bhramarraj
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AS QC JH KD

JD KS AC QH

KC JS QD AH

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

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AS QC JH KD

JD KS AC QH

KC JS QD AH

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.

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HA SK DJ CQ

CJ DQ SA HK
SQ HJ CK DA
DK CA HQ SJ
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nice. now how many different 'correct' answers are there?

HA SK DJ CQ

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

AS QC JH KD

JD KS AC QH

KC JS QD AH

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

As Kh Qd Jc

Jd Qc Ks Ah

Qh Js Ac Kd

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

Excluding rotations and mirror images,

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.

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