A4. Three different numbers from the set $\{1,2,3,4,5,6,7,8,9\}$ are placed in the top three squares of the figure below. Then the numbers are added according to the indicated scheme. Let the largest possible number that can appear in the bottom square be Max and the smallest possible number that can appear in the bottom square be Min. What is the value of Max - Min?
(A) 16
(B) 24
(C) 25
(D) 26
(E) 32

![](https://cdn.mathpix.com/cropped/2024_04_17_8dd363468b37c79bb3bag-1.jpg?height=323&width=333&top_left_y=2308&top_left_x=1663)
A4. Three different numbers from the set $\{1,2,3,4,5,6,7,8,9\}$ are placed in the top three squares of the figure below. Then the numbers are added according to the indicated scheme. Let the largest possible number that can appear in the bottom square be Max and the smallest possible number that can appear in the bottom square be Min. What is the value of Max - Min? (D) 26

Solution If we place $a, b$, and $c$ in the top three squares, the result is $a+2 b+c$. The largest result is obtained by taking the largest possible numbers for $b$ and then for $a$ and $c$. $b=9$, $a=8$, and $c=7$ gives a result of 33. The smallest result is obtained by taking the smallest possible numbers for $b$ and then for $a$ and $c$. $b=1, a=2$, and $c=3$ gives a result of 7. The difference is $33-7=26$. $\square$

![](https://cdn.mathpix.com/cropped/2024_04_17_cb8708f0b7aaf218de84g-1.jpg?height=309&width=307&top_left_y=1320&top_left_x=1668)