This sounds like a Pascal's triangle question or binomial expansion where you add up all the coefficients.

almost 8 layers, 97 bricks needed for 7 layers, 177 for 8, 6 bricks short of 8 layers

or alternatively, lop off the top 3 layers, and you've got 170 bricks for the

lower 5 layers. One brick more than needed for those 5 layers.

Depending on how you interpret the question, it's somewhere between 5+ and 8 layers. Minimum 5, maximum nearly 8.

first line of Pascal's triangle is 1

2nd line is 11 2+1=3 3

3rd is 121 4+3= 7

4th is 1331 8+7= 15

5th 14641 16+15 =31

6th 151051 22+31= 53

7th 16-15-15-61 44+53= 97

8th 17-21-30-21-71 =88+97=177

this is the same as finding all the coefficients of the binomial expansion of (x+y)^{n} with n varying between 1 and 8, and finding the coefficients of each term.

That may be as triangular as you can get from rectangular bricks.