Fill in numbers in the boxes below so that the sum of the entries in each three consecutive boxes is $2005$. What is the number that goes into the leftmost box?

[asy]
size(300);
label("999",(2.5,.5));
label("888",(7.5,.5));

draw((0,0)--(9,0));
draw((0,1)--(9,1));
for (int i=0; i<=9; ++i)
{
draw((i,0)--(i,1));
}
[/asy]
1. Let's label the boxes \( A, B, C, D, E, F, G, H, I \) from left to right. We are given that \( B = 888 \) and \( C = 999 \).

2. According to the problem, the sum of the entries in each three consecutive boxes is \( 2005 \). Therefore, we can write the following equations:
   \[
   A + B + C = 2005
   \]
   \[
   B + C + D = 2005
   \]
   \[
   C + D + E = 2005
   \]
   \[
   D + E + F = 2005
   \]
   \[
   E + F + G = 2005
   \]
   \[
   F + G + H = 2005
   \]
   \[
   G + H + I = 2005
   \]

3. Substitute the known values \( B = 888 \) and \( C = 999 \) into the first equation:
   \[
   A + 888 + 999 = 2005
   \]
   Simplify to find \( A \):
   \[
   A + 1887 = 2005
   \]
   \[
   A = 2005 - 1887
   \]
   \[
   A = 118
   \]

4. To ensure consistency, let's find the values of \( D, E, F, G, H, \) and \( I \) using the given conditions:
   - From \( B + C + D = 2005 \):
     \[
     888 + 999 + D = 2005
     \]
     \[
     1887 + D = 2005
     \]
     \[
     D = 2005 - 1887
     \]
     \[
     D = 118
     \]

   - From \( C + D + E = 2005 \):
     \[
     999 + 118 + E = 2005
     \]
     \[
     1117 + E = 2005
     \]
     \[
     E = 2005 - 1117
     \]
     \[
     E = 888
     \]

   - From \( D + E + F = 2005 \):
     \[
     118 + 888 + F = 2005
     \]
     \[
     1006 + F = 2005
     \]
     \[
     F = 2005 - 1006
     \]
     \[
     F = 999
     \]

   - From \( E + F + G = 2005 \):
     \[
     888 + 999 + G = 2005
     \]
     \[
     1887 + G = 2005
     \]
     \[
     G = 2005 - 1887
     \]
     \[
     G = 118
     \]

   - From \( F + G + H = 2005 \):
     \[
     999 + 118 + H = 2005
     \]
     \[
     1117 + H = 2005
     \]
     \[
     H = 2005 - 1117
     \]
     \[
     H = 888
     \]

   - From \( G + H + I = 2005 \):
     \[
     118 + 888 + I = 2005
     \]
     \[
     1006 + I = 2005
     \]
     \[
     I = 2005 - 1006
     \]
     \[
     I = 999
     \]

5. All values are consistent with the given conditions. Therefore, the leftmost box \( A \) is \( 118 \).

The final answer is \( \boxed{118} \).