9 replies to this topic

[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).

[vistaptb]

Spoiler for Easy

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]

Spoiler for Easy

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)

Spoiler for nice try but...

your diagonals don't meet the requirement of the op

Edited by BMAD, 08 March 2013 - 04:51 AM.

[bonanova]

Spoiler for How about

 

As Kh Qd Jc

Jd Qc Ks Ah

Kc Ad Jh Qs

Qh Js Ac Kd

 

[bhramarraj]

Spoiler for what about this

AS QC JH KD

JD KS AC QH

KC JS QD AH

QH AD KS JC

Edited by bhramarraj, 08 March 2013 - 08:55 AM.

[bhramarraj]

Spoiler for what about this

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]

Spoiler for what about this

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]

Spoiler for how about?

HA SK DJ CQ
CJ DQ SA HK
SQ HJ CK DA
DK CA HQ SJ

[BMAD]

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

Spoiler for how about?

HA SK DJ CQ
CJ DQ SA HK
SQ HJ CK DA
DK CA HQ SJ

 

 

Spoiler for what about this

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.

 

 

Spoiler for How about

 

As Kh Qd Jc

Jd Qc Ks Ah

Kc Ad Jh Qs

Qh Js Ac Kd

 

[bonanova]

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

 

Excluding rotations and mirror images, 

 

Spoiler for I believe

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.