This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

Tags were heavily modified to better represent problems.

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Found problems: 2

2024 AMC 10, 6
Tags: 1969 AHSME , 1984 AIME
What is the minimum number of successive swaps of adjacent letters in the string ABCDEF that are needed to change the string to FEDCBA? (For example, 3 swaps are required to change ABC to CBA; one such sequence of swaps is ABC $\rightarrow$ BAC $\rightarrow$ BCA $\rightarrow$ CBA.) $ \textbf{(A) }6 \qquad \textbf{(B) }10 \qquad \textbf{(C) }12 \qquad \textbf{(D) }15 \qquad \textbf{(E) }24 \qquad $

1969 AMC 12/AHSME, 23
Tags: factorial , number theory , prime numbers , AMC , 1969 AHSME , Ahsme , AMC 12
For any integer $n$ greater than $1$, the number of prime numbers greater than $n!+1$ and less than $n!+n$ is: $\textbf{(A) }0\qquad \textbf{(B) }1\qquad \textbf{(C) }\dfrac n2\text{ for }n\text{ even,}\,\dfrac{n+1}2\text{ for }n\text{ odd}$ $\textbf{(D) }n-1\qquad \textbf{(E) }n$