Reverse Pascal Triangle

We will use the corresponding lowercase letters to the bricks assigned to them; the top layer is layer 1, the layer below is layer 2, and so on.

Layer $4$ :

$137 + b = f$

$52 + b = g$

$52 + d = h$

$d + e = 147$

Layer $3$ :

$f + g = j \rightarrow 137 + 52 + 2b = j \rightarrow 189 + 2b = j$

$g + h = 225 \rightarrow 52 + b + d + 52 = 225 \rightarrow b + d = 121$

$h + 147 = l \rightarrow 52 + d + 147 = l \rightarrow 199 + d = l$

Layer $2$ :

$j + 225 = m \rightarrow 189 + 2b + 225 = m \rightarrow 414 + 2b = m$

$225 + l = n \rightarrow 225 + 199 + d = n \rightarrow 424 + d = n$

Layer $1$ :

$m + n = 978 \rightarrow 2b + d + 838 = 978 \rightarrow 2b + d = 140$

Now, we have a system of equations:

$\begin{cases} b + d = 121 \\ 2b + d = 140 \end{cases}$

Substituting the first equation in the second yields:

$b + 121 = 140 \rightarrow b = 19$ , which is the sought answer.

The format of the bricks will be similar to the Pascal's Triangle

From O and K:

O = A + 4B + 6C + 4D + E

K = B + 2C + D

Substituting given values we can get :

382 = 4B + 3D

121 = B + D

Given those two equations we get B = 19, D = 102

Writing the top layer in terms of the bottom layer:

978 = A + 4B + 6C + 4D + E

978 = A + B + 3(B + 2C + D) + (D + E)

978 = A + B + 3K + I

978 = 137 + B + (3x225) + 147

Therefore, B = 978 - 959

B = 19

So the way to do this is to take $B$ as $x$ , and find all the other boxes in terms of $x$ and hope for your answer to come soon,

$B = x$

First of all, $F = 137+x$

$G=52+x$

$J=189+2x$

$M=414+2x$

And then, $K=G+H \Rightarrow H = 173 - x$

$L=320-x$

$N=545-x$

And finally. $M+N=O \Rightarrow \boxed{x=19}$

M + N = 978 = J + L + 2(225)

J + L = 528 ............................... (1)

G + H = 225 ..............................(2)

J + L + 225 = 2(G + H) + F + 147 .......................(3)

From (1), (2) and (3)

F = 156

F = 137 + B

B = 19

G + H = 225, B - D = G - H, SINCE (D = 140 - 2B) AND (H = 225 - G), B - (140 - 2B) = G -(225 - G), 3B - 140 = 2G - 225, SINCE (B = G - 52), 3(G - 52) - 140 = 2G - 225 >>> G=71,

THE REST IS HISTORY.

F=137+B

G=52+B

J=189+2B

M=414+2B

O=414+2B+N

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H=52+D

L=199+D

N=424+D

O=838+2B+D

2B+D=140

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G+H=225

52+B+52+D=225

B+D=121

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2B+D=140

B+D=121

--------(-)

B = 19