In the picture, there is a rounding addition pyramid. Each brick (except those from the bottom row) should contain the sum of the numbers written on the two adjacent bricks from the lower row, but appropriately rounded: sums in the second row from the bottom are rounded to the tens, in the third row to the hundreds, and in the highest fourth row to the thousands. Fill in the empty bricks of the pyramid with the largest possible whole numbers.

![](https://cdn.mathpix.com/cropped/2024_04_17_5cf185c692e63b89ed09g-2.jpg?height=251&width=594&top_left_y=1828&top_left_x=754)
Let's mark the free spaces in the pyramid with the letters $A, B, C, D$:

| $A$ | $A$ |  |  |  |
| :--- | :--- | :--- | :--- | :--- |
| 1100 | 1800 |  |  |  |
| 440 |  | $B$ | 1070 |  |
| 188 | $C$ | 451 | $D$ |  |

First, we determine the highest possible values of $A$ and $D$.

Value of $A$:

$1100 + 1800 = 2900$, which, when rounded to the nearest thousand, gives $A = 3000$.

Value of $D$:

From the equation $D + 451 \doteq 1070$ (rounding to the nearest ten), we get the condition $614 \leqq D \leqq 623$, so the highest possible value of $D$ is $D = 623$.

Value of $B$:

Two conditions must be satisfied, which come from the equations:

$B + 440 \doteq 1100$ (rounding to the nearest hundred), from which $610 \leqq B \leqq 709$,

$B + 1070 \doteq 1800$ (rounding to the nearest hundred), from which $680 \leqq B \leqq 779$.

The number $B$ must be a whole multiple of ten, so $B \leqq 700$.

Value of $C$:

Two conditions must be satisfied, which come from the equations:

$C + 188 \doteq 440$ (rounding to the nearest ten), from which $247 \leqq C \leqq 256$,

$C + 451 \doteq B$ (rounding to the nearest ten), from which $B - 456 \leqq C \leqq B - 447$.

We already know that $B \leqq 700$, so $C \leqq B - 447 \leqq 253$. When $B = 700$, $C = 253$ satisfies both conditions, so it is the highest possible value, and we have confirmed that the highest possible value of $B$ is $B = 700$.

![](https://cdn.mathpix.com/cropped/2024_04_17_5cf185c692e63b89ed09g-3.jpg?height=254&width=585&top_left_y=1209&top_left_x=764)

[ 1 point for determining $A$, 2 points for determining $B$, 2 points for determining $C$, 1 point for determining the value of $D$ ]