2026 AMC 8 Problem 2

Attempt Problem 2 of the 2026 AMC 8 below, then check your answer against the video solution and professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2026 AMC 8 solutions, or check the answer key.

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2.

In the array shown below, three 33s are surrounded by 22s, which are in turn surrounded by a border of 11s. What is the sum of the numbers in the array?
11111111222221123332112222211111111 \begin{array}{ccccccc} 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{array}
4949
5151
5353
5555
5757
Answer: C
Concepts:basic counting
Small hint:
Count how many entries are 11, 22, and 33
Big hint:
Use a weighted sum: 1⋅#1+2⋅#2+3⋅#31\cdot\#1+2\cdot\#2+3\cdot\#3
Video solution:
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Written solution:
There are 2020 border entries equal to 11, 1212 entries equal to 22, and 33 entries equal to 33. The sum is 20⋅1+12⋅2+3⋅320\cdot1+12\cdot2+3\cdot3 =20+24+9=20+24+9 =53=53.
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