A box contains 105 candies packed in rows, columns, and layers. How many layers of candies are in the box?

Answer 1

Layers*Columns*Rows = 105

105 = 5*7*3

That means that there are either seven layers of 5x3, five layers of 7x3 or three layers of 5x7.

The only combination that really makes sense is three layers.

Looking at the other answers, I see that you could have 1x1x105. Having one layer of 105x1 doesn't make sense either. However, if the candies are something like NECCO wafers, you could have 105 layers of one -- but they usually come in a roll, not a box.

Answer 2

Without additional information, I will make a few assumptions. 1. I assume there is more than one layer, row and column. 2. I assume that all layers, rows and columns have the same quantity and no pieces are missing. 3. I assume that they are striving for the least possible number of layers, rows and columns to achieve the desired quantity of 105 pieces. 4. I assume that they are trying to keep packaging as close to square as possible because it's easier to keep inventory that way.

So, that said, we find the highest whole number that evenly divides into 105. 105 = 3 x 35.

So, we now know that we have 3 layers of 35 candies per layer.

The closest we can get to a square with 35 candies is to have 5 rows of 7 columns. Or 5 columns of 7 rows, I suppose.

So, if you follow my reasoning, you have 5 rows, 7 columns and 3 layers.

You could also make an argument for 3 rows of 35 columns in 1 layer, and possibly others, but I think I'm probably closer to the answer you'd be looking for.

Answer 3

105 has 3 prime number factors 5, 3 and 7 which can be regarded as layer, row and column.

Layer can be either 5 or , 3 or 7

So answer is either 5, or 3 or 7!

Regards

Answer 4

105 = 1∙3∙5∙7
The box has one of these dimensions:

1×1×105
1×3×35
1×5×21
1×7×15
3×5×7

Of these, 3×5×7 uses the least box material. So I'd say there are 3 layers. Not 5 layers or 7 layers, because I would keep the center of gravity low. Less likely for stacks to fall over.

Answer 5

It depends how the box is shaped.
105 = 1*1*105
If each column is one candle wide, and each row is 105 candles, that there is one layer.
Or each row could be one candle long, and there would still be one layer.
Or there could be 105 layers of one candle each.

105 also = 3*5*7
So each row could be 5, each column 3, and there would be seven layers.
Or each row could be 3, each column 5, and there would be seven layers.
Or each row could be 5, each column 7, and there would be Three layers.
Or each row could be 7, each column 5, and there would be three layers.
Or each row could be 3, each column 7, and there would be five layers.
Or each row could be 7, each column 3, and there would be five layers.

3*35*1 = 105

It could also be row could be 35, each column 3, and there would be one layer.
Or each row could be 3, each column 35, and there would be one layers.
Or each row could be 35, each column 1, and there would be three layers.
Or each row could be 1, each column 35, and there would be three layers.
Or each row could be 3, each column 1, and there would be thirty-five layers.
Or each row could be 1, each column 3, and there would be thirty-five layers.

21*5*1 = 105
Each row could also be 21, each column 5, and there would be one layer.
Or each row could be 5, each column 21, and there would be one layers.
Or each row could be 21, each column 1, and there would be five layers.
Or each row could be 1, each column 21, and there would be five layers.
Or each row could be 5, each column 1, and there would be twenty-one layers.
Or each row could be 1, each column 5, and there would be twenty-one layers.

7*15*1 = 105
This leads to an additional six possibilities in the same vein as the others.

Those are all the possibilities that don't allow for partial candles in rows, columns, or layers. There are 27 arrangements and eight different answers for the number of layers in all.

Answer 6

7 rows 5 columns and 3 layers

Answer 7

7 Layers of candy 3 rows per layer, 5 columns.

Answer 8

3

Answer 9

3 x 5 x 7
only possible combination, being the prime factors of 105


ANS: the "layer" value woudl depend on which way you are looking at the box, either 3 layers, or 5 layers or 7 layers.

Answer 10

It could be:

3 layers
35 in each layer
5 rows of 7 in each layer

Answer = 3 layers