Solution: Building With Bricks Math Puzzle

There are a number of different ways that students have solved this puzzle.

Marisa's Solution

I found some sugar cubes and used them to build several pyramids. I had only about 30 cubes, so I had to keep reusing the same cubes. After a few tries I found a shortcut. After I built one pyramid, I’d build the next base, then pick up the previous pyramid and place it on the base. As I was doing this, I noticed that I had to add 2 more bricks for each new base than for the base of the previous pyramid.

I kept track of my results in a table:

I noticed that the number of bricks kept increasing by 2, so I knew that after a pyramid of height 5, I had to add 11 bricks for a pyramid of height 7, add 13 to that for a pyramid of height 7, and so forth, so I worked my way up to 10. I didn’t build any more pyramids because I was out of cubes.

So my rule is: If you know how many bricks you used for one pyramid, you have to add 2 more bricks than you added the last time, to get the next pyramid.

Sampen's Solution

I used graph paper to work out my solution. I made drawings of five pyramids.

Then I made a table.

I could see from the table that B is always H x H or B = H2. Then I drew another pyramid 6 bricks high. It needed 36 bricks, which is 6 x 6.

So my rule is correct.

Andre's Solution

I used square tiles to build my pyramids. I noticed that after I built a pyramid, I could always rearrange the tiles into a square. What I did was take away all the tiles to the right of the middle stack and move them all over to the left. They always fit in and make a square. The height of the square is the same as the height of the pyramid. So the number of square tiles is the same as the area of the square or H x H. The rule for the architect is B = H x H.

Here are some examples:

H = 2, area of big square = 2 x 2 = 4
 

H = 3; area of big square = 3 x 3 = 9
 

H = 6; area of big square = 6 x 6 = 36