Brick puzzle

Problem

Given bricks of 1x1x4, and a box of 6x6x6, can you fit 53 of the bricks into the box?

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Hints

Hint 1

$6\cdot6\cdot6 = 216$

$216/4 = 54$

Hint 2

Visualize by layers of the puzzle box, for each layer, how many can fit?

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Solution

Show Solution

No

Show Explanation

Let's visualize the problem by following the diagram. The left is an empty box. And in the middle, you can see the red stripes representing the bricks occupying space in a layer of the box. Each layer can only contain a maximum of 8 bricks. 8 times 6 is 48 so 48 base bricks can be arranged in that way. And as you can see for a layer, there are 4 unoccupied slots. Tower them up 6 blocks, and you can fit only 4 of them. Thus 48+4=52 is the maximum number of bricks you can place. And hence you can't place 53 bricks into the box.