2026 AMC 8 Problem 12
Attempt Problem 12 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.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
12.
In the figure below, each circle will be filled with a digit from to Each digit must appear exactly once. The sum of the digits in neighboring circles is shown in the box between them. What digit must be placed in the top circle?
it is impossible to fill the circles
Answer: D
Small hint:
Let the top digit be
Big hint:
The two adjacent upper digits are and
Video solution:
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Written solution:
Let the top digit be . Moving clockwise from the top, the other digits are , , , , and . For these six values to be exactly , the value works and gives the set . Thus the top digit is .
Problem 12 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
- 1988 AMC 8
- 1989 AMC 8
- 1990 AMC 8
- 1991 AMC 8
- 1992 AMC 8
- 1993 AMC 8
- 1994 AMC 8
- 1995 AMC 8
- 1996 AMC 8
- 1997 AMC 8
- 1998 AMC 8
- 1999 AMC 8
- 2000 AMC 8
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- 2006 AMC 8
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- 2022 AMC 8
- 2023 AMC 8
- 2024 AMC 8
- 2025 AMC 8