AMC 8 2026 (Problem 2)In the array shown below, 3s are surrounded by 2s, which are then surrounded by a border of 1s. What is the sum of the numbers in the array?11111111222221123332112222211111111\begin{matrix}1&1&1&1&1&1&1\\ 1&2&2&2&2&2&1\\ 1&2&3&3&3&2&1\\ 1&2&2&2&2&2&1\\ 1&1&1&1&1&1&1\end{matrix}11111122211232112321123211222111111(A) 49\text{(A)}\;49(A)49(B) 51\text{(B)}\;51(B)51(C) 53\text{(C)}\;53(C)53(D) 55\text{(D)}\;55(D)55(E) 57\text{(E)}\;57(E)57Hints (4)Hint 1Number of 3s=n3=3\text{Number of 3s}=n_3=3Number of 3s=n3=3Hint 2n2=3×5−3=12n_2=3\times5-3=12n2=3×5−3=12Hint 3n1=5×7−3×5=35−15=20n_1=5\times7-3\times5=35-15=20n1=5×7−3×5=35−15=20Hint 4Ans=3n3+2n2+n1=9+24+20=53\text{Ans}=3n_3+2n_2+n_1=9+24+20=53Ans=3n3+2n2+n1=9+24+20=53Final Answer(C) 535353