Building Bricks

A child is playing with building bricks like this one.
He decides to build the simple tower shown.

How many bricks would he
need to build this tower?

If the last column was
14 bricks high how many bricks would he
need?

If the last column was 50 bricks high
how many bricks would he need now?

sorry - not shown

To determine how many bricks are needed to build these towers, we first need to understand the pattern. Let's analyze the first tower as an example.

In the first tower, we can observe that the height of each column decreases by 1 brick as we move from left to right. The first column has 6 bricks, the second column has 5 bricks, the third column has 4 bricks, and so on. To find the total number of bricks in this tower, we can sum up the heights of each column.

For the first tower, where the last column is 14 bricks high:
First, let's determine the height of each column:
- The first column has 6 bricks
- The second column has 5 bricks
- The third column has 4 bricks
- The fourth column has 3 bricks
- The fifth column has 2 bricks
- The last column has 14 bricks

To find the total number of bricks, we add up the heights of each column:

Total bricks needed = 6 + 5 + 4 + 3 + 2 + 14
Total bricks needed = 34

So, to build the first tower with a 14-brick high last column, you would need 34 bricks.

For the second tower, where the last column is 50 bricks high:
The pattern for this tower remains the same, with the height of each column decreasing by 1 brick from left to right. However, we now need to find the total number of bricks when the last column is 50 bricks high.

We can use the same approach as before:
- The first column has 6 bricks
- The second column has 5 bricks
- The third column has 4 bricks
- The fourth column has 3 bricks
- The fifth column has 2 bricks
- The last column has 50 bricks

Total bricks needed = 6 + 5 + 4 + 3 + 2 + 50
Total bricks needed = 70

So, to build the second tower with a 50-brick high last column, you would need 70 bricks.