Half your age plus seven
At twenty the rule allows 17 to 26; nine years wide. At forty it allows 27 to 66, a span of thirty-nine. At sixty it runs from 37 to 106. The widening is the rule most defensible feature: it reflects the reasonable observation that a five-year gap matters far more at twenty than at sixty.
The rule gives a lower bound of half your age plus seven and an upper bound of your age minus seven, doubled. At 30 that is 22 to 46. A range that widens steadily as you get older.
How the rule works
Its one genuinely interesting property is symmetry: the upper bound is the exact inverse of the lower, so the relation is mutual. At 30 the lower bound is 22, and 22’s own upper bound is (22 − 7) × 2 = 30. Exactly back where you started. If someone falls inside your range, you fall inside theirs, and very few folk rules survive that test. The width has a tidy formula too. Subtract the bounds and what is left is one and a half times your age minus 21: nine years at twenty, 39 at forty, 69 at sixty. Setting that to zero shows precisely where the rule gives out. At 14 both bounds are exactly 14 and the range is a single year wide; below 14 they cross over, so a thirteen-year-old is handed a lower bound of 13.5 against an upper bound of 12. The rule is not merely unhelpful for children, it is arithmetically empty for them.
Questions
22 to 46.
It turns up in print as social advice well over a century ago. There is no research behind it and never was.
Yes; the upper bound is the exact inverse of the lower, so if you are inside their range they are inside yours.
By one and a half years per year of age. The width is 1.5 times your age, minus 21.
At 14 the range collapses to a single year, and below 14 the bounds cross and it allows nothing at all.
From 14 upward, yes. The lower bound only climbs above your own age below 14, which is exactly where the rule stops working.
No. It is a saying with convenient arithmetic, and the arithmetic is the only part of it that can be checked.