Logical Problems

The commonest order question gives one person's place from each end of a row and asks how many people the row holds, or gives two people's ranks and asks how many sit between them. Both are decided by counting the ends correctly. If someone is $l$-th from the left and $r$-th from the right of a row of $N$, that person has been counted twice, once in each total, so

$$N = l + r - 1.$$

For a between item, convert both ranks to positions from the same end and subtract the two ranks and one more, because the people at both ends are excluded from the gap.

Order also appears as a chain of comparisons. Where several people are compared, the answer is the person at the end of the chain that has the most links pointing away from them. A statement that A is older than B but younger than F, and that C is younger than B but older than D, writes itself as $F > A > B > C > D$, so D is youngest with no further information needed. The same chain decides a seniority appointment: list the comparisons, drop any candidate who removes themselves, and the most senior of those left is the answer.