A dictionary of Confusable Phrases: More Than 10,000 Idioms and Collocations

give someone a run • give someone the run
give someone a run —(coll.) 
1
. see whether smb. is suitable
for a job, etc. by letting the person do it for a short time: She’s
not someone I would normally date, but I’ll give her a run.
2. offer a strong challenge or competition to a person: John
came in second but certainly gave her a run for most sales this
quarter.
Note: 
The expression does not fully correlate in meaning with
the phrase give someone a run for his money—
1
. give someone
a run 2: There was no obvious Democratic candidate poised
to give Kyl a run for his money. 2. derive much satisfaction in
return for one’s outlay or efforts: Well if anything has ever given
me a run for my money, this morning definitely took the cake.
give someone the run —(of ) give a person permission to use
smth. freely: Frank generously gave me the run of his extensive
library.
Note: 
The expression does not correlate in meaning with the
phrase give someone the runs—(coll.) cause diarrhea: These
pills won’t help and only give her the runs.
give someone a run-down • run someone down
give someone a run-down —(coll.) give a person a brief survey
of facts (also: give someone a run-through): After she gave me
a rundown of her “typical day,” it was apparent why she was
exhausted.
Note: 
The expression is not equivalent in meaning to the phrase
run it down to someone—(U.S. sl.) describe or explain a sit-
uation; tell a person the whole truth about smth.: I tried to figure
out the best way to run it down to this girl that they didn’t
have to live in this town.
run someone down —
1
. (also: run someone over) knock smb.
to the ground with a vehicle (usually Passive): He was run
down by a vehicle operated by another member of the staff.
2. speak of a person in a disparaging or critical manner: I wish
you’d stop running me down all the time. I resent it, and I
won’t stand for it. 3. find or capture smb. after a long search
or chase: The airport police finally ran him down at the far
end of the Lost Luggage hangar.