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2025 AMC 8 Problems/Problem 21: Difference between revisions

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==Problem 21==
 


The Konigsberg School has assigned grades 1 through 7 to pods <math>A</math> through <math>G</math>, one grade per
The Konigsberg School has assigned grades 1 through 7 to pods <math>A</math> through <math>G</math>, one grade per

Revision as of 21:59, 29 January 2025


The Konigsberg School has assigned grades 1 through 7 to pods $A$ through $G$, one grade per pod. Some of the pods are connected by walkways, as shown in the figure below. The school noticed that each pair of connected pods has been assigned grades differing by 2 or more grade levels. (For example, grades 1 and 2 will not be in pods directly connected by a walkway.) What is the sum of the grade levels assigned to pods $C, E$, and $F$?


$\textbf{(A)}~12\qquad\textbf{(B)}~13\qquad\textbf{(C)}~14\qquad\textbf{(D)}~15\qquad\textbf{(E)}~16$

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