14. On an island, there are 2023 people standing in a line, each of whom is either a knave or a knight: knights always tell the truth, while knaves always lie. If $i$ is odd, the person in the $i$-th position exclaims: "There are at least $i$ knaves"; if $i$ is even, the person in the $i$-th position exclaims: "There are exactly $i$ knaves". How many knaves are there?
14. The answer is 1348. If the number of scoundrels is odd, say $2 m+1$, then the people telling the truth are all and only those in odd positions less than or equal to $2 m+1$, which are $m+1$. There would thus be $2 m+1$ scoundrels and $m+1$ knights, for a total of $3 m+2$ people, but this is impossible since the equation $2023=3 m+2$ leads to $m=\frac{2021}{3}$, which is not an integer. The scoundrels are therefore an even number, say $2 m$: the knights will be all and only the people in odd positions less than or equal to $2 m$, plus the person in position $2 m$, so in total $m+1$. Thus $3 m+1=2023$ and therefore the scoundrels are $2 m=1348$. It is verified that the configuration works.