Maximum no. of laddoos of diameter $6$cm in a box of given dimension

Question

What is the maximum number of laddoos having diameter of $6\text{ cm}$ that can be packed in a box whose inner dimensions are $24\times 18\times 17\text{ cm$^3$}$.

I found that at the lower label maximum $12$ laddoos can be placed, and at the next upper label maximum $12$ laddos can be placed , and at the upper label maximum $6$ laddoos can be placed. So total $12+12+6=30$ laddoos can be packed. But the given answer contradict my answer.

Please tell me where my fallacy ?

Answer 1

Think of us looking at one wall of the packing. (Not the floor, but a side wall). You can pack 4 along the bottom and top and put 3 in between them. See (crude) attached image. Then you can repeat this wall 3 times in the 18cm direction.

ETA: We know we can get away with this spacing vertically (the 17cm direction) because hexagonal circle packing gives is a layer height of appx $0.902414d$

Answer 2

I found that at the lower label maximum 12 laddoos can be placed, and at the next upper label maximum 12 laddos can be placed , and at the upper label maximum 9 laddoos can be placed. So total 12+12+9=33 laddoos can be packed. which is the exect ans according to me