There are #77# right-angled blocks of dimensions #3xx3xx1#. Is it possible to place all these blocks in a closed rectangular block of dimensions #7xx9xx11#?

Answer 1

No.

Call a #1 xx 1 xx 1# component a cell.
Consider a #7 xx 11 xx 1# slice of the rectangular block.
Each #3 xx 3 xx 1# block intersects it in one of three ways:
Not at all. In which case it contributes #0# cells.
Edgewise. In which case it contributes #3# cells.
Full. In which case it contributes #9# cells.
In any of these three cases, the number of cells in the slice contributed by each #3 xx 3 xx 1# block is a multiple of #3#.
In order to fill the slice, we need #7 xx 11 = 77# cells filled, which is not a multiple of #3#.
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Answer 2

Yes, it is possible to place all 77 right-angled blocks of dimensions 3x3x1 inside a closed rectangular block of dimensions 7x9x11. The volume of the larger rectangular block is 7 x 9 x 11 = 693 cubic units, and the volume of each small block is 3 x 3 x 1 = 9 cubic units. Since 77 x 9 = 693, the total volume of the small blocks matches the volume of the larger block, indicating that it is possible to arrange them to fit perfectly within the larger block without leaving any gaps.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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