Correct solutions were received from Sheila and Kirsty from Madras College, both of whom sent in excellent solutions that explained the logical sequence of steps they took to find the solution. I have used Sheila's solution as the basis of what follows so well done to both of you. Correct solutions were also received from Steven Lou of Riccarton High School; Claire and Nicholas from Hillingdon and Rohan (looks like you are a Liverpool fan - this must be worth a mention).

Due to statement B, a queen can only go in boxes 3,4 and 6. It cannot go in boxes 1, 2, 5, 7 or 8 because those boxes are not between two other boxes.

first solution

If the Queen was in box 3 then, due to statement B, two kings would have to go in boxes 2 and 4.

Due to statement C, two jacks would have to go in boxes 1 and 6.

But due to statement G another king would have to go in the diagram on the border of one of the other kings and that isn't possible.

solution card 2

If the queen is in box 6; due to statement B two kings would have to go in boxes 5 and 7 or 4 and 8. Looking first at the king in boxes 5 and 7.

Due to statement C, two jacks would have to go on either side of a king and since this is not possible using the kings in 5 and 7 the only option would be to put another king in box 3 and put two jacks in 2 and 4.

However, due to statement D this is not a possibility as it would leave the jack in box 4 bordering the queen in box 6.

 

solution 3

Continuing the second possibility from above with the two kings in boxes 4 and 8.

Due to statement C two jacks would have to go on either side of a king, but that is not possible with the kings in boxes 4 and 8.

There is not a place left on the grid where it is possible to put another king so that it can lie between two jacks.

This arrangement is also not possible.

 

solution four

If the queen is in box 4 then, due to statement B, two kings are needed in boxes 1 and 6.

Due to statement C, two jacks must go in boxes 5 and 7.

It is also possible to put jacks in boxes 2 and 8 - due to statement D they cannot go beside a queen.

From statement E we know there is only one ace and since an ace cannot border a king (statement F) there are only two possible places for an ace - boxes 2 and 3.

Due to statement G, a king has to go in box 8 otherwise you would need two more kings to satisfy statement G and they could only go in boxes 2 and 3, leaving no room for the ace.

So we now have to deal with boxes 2 and 3:

Another king could now be placed in either box 2 or box 3 (but not both - see above). However this would be illegal as it would then be next to an ace, which is not allowed (statement F).

Another Queen could be placed in box 3, but it would then border a Jack, which is an illegal move (statement D).

So the only possibilities left are for Aces and/or Jacks in boxes 2 and 3. There are four possibilities:
JJ (there would then be no ace - breaks statement E)
AA (there would then be two aces - breaks statement E)
AJ (a jack would border a queen - breaks statement D)
JA

Therefore the only one that fulfils all the criteria is JA, so the solution is:

final solution