Start with the fixed clue
Most arrangement puzzles have one clue that fixes a position: "C sits in the middle", "P is at the left end". Place that first, then add the clues that refer to already-placed people. Leave "not next to" clues for last; they usually decide between the remaining options.
Linear rows
When people face north (towards the top of the page, the same way you face when reading it), their left is your left. When they face south, towards you, their left is your right.
Number the seats 1, 2, 3 … from the left and fill them in.
Example. Five people sit in a row facing north. C is in the middle, A is immediately to C's left, E is at the right end, and B is not at an end.
C is in seat 3 and A in seat 2.
E is in seat 5.
B can't be at an end, so B is in seat 4, leaving D in seat 1.
The row is D, A, C, B, E.
Circular tables
When people sit around a table facing the centre, a person's left is the next seat clockwise when you look down on the table. If they face outwards, it is anticlockwise.
With four people around a square table, opposite seats are two places apart.
Ranking and positions
For a row or rank list of n people:
position from the right = n − position from the left + 1
if someone is p-th from the top and q-th from the bottom, n = p + q − 1
people between positions a and b (a < b) = b − a − 1
someone k-th from both ends means n = 2k − 1
Example. In a row of 40, the 15th from the left is 40 − 15 + 1 = 26th from the right.
Shortcuts and tricks
The standard way is to draw the seats and fill in the fixed clues first. For ranking questions, three formulas replace the drawing.
Position from the other end
Example: 30 in a row; Tara is 12th from the left. Her position from the right?
Standard way: 11 people are to her left, so 30 − 11 − 1 = 18 are to her right. She is 19th from the right.
Shortcut: from the right = total − from the left + 1 = 30 − 12 + 1 = 19.
Total from both ends
Example: 9th from the top and 14th from the bottom.
Standard way: 8 above, 13 below, plus the person: 8 + 1 + 13 = 22.
Shortcut: total = top + bottom − 1 = 9 + 14 − 1 = 22.
How many between
Example: positions 6 and 19 in a queue.
Standard way: list positions 7 to 18: that is 12 people.
Shortcut: between = larger − smaller − 1 = 19 − 6 − 1 = 12.
Left and right around a table
For people facing the centre, a person's left is the next seat clockwise and their right is the next seat anticlockwise. For people facing outwards, it is the other way round.
Exam tips
Draw the row or table once and fill it in; don't re-read the clues each time.
Note facing direction before using left and right.
When two arrangements fit, check every clue again; usually one breaks a "not next to" condition.