# "all but at most one" - What does it mean?

I came around this one just now and I can't tell the meaning of this sentence by the context.

no new vehicle is used unless all but at most one other vehicle has at least 50% of its time scheduled

Does it mean something like "all are, but one is not"?

• I suppose it means there is never more than one vehicle with 50% or less of its time scheduled, am I right ? Commented Jan 24, 2012 at 23:49
• +1 for bringing us such a laughable example of poor writing. D- ;) Commented Jan 24, 2012 at 23:53
• I think it means a new vehicle is not used if two or more others are more than 50% free. Commented Jan 25, 2012 at 0:00
• ...perhaps the writer is a fan of Bertrand Russell, whose note to the milkman said In general, please leave a set of bottles equal in number to the set of empty bottles on the step, except where the latter set is null, in which case leave one bottle, reducing by that number the delivery on the next occasion if and only if two or more bottles are present. Commented Jan 25, 2012 at 0:05
• Specifically, all but at most one simply means all, or all except one. That's the easy bit! But I'm afraid I think the question is a bit too localised. Commented Jan 25, 2012 at 0:07

"At most one" means zero or one.

"All but at most one" means "all" (all minus zero) or "all but one" (all minus one).

But wow, what a confusing sentence!

• Think of "all but one", and then allow for the case of zero. "All but at most one". But wow, awkward wording.
– Jay
Commented Jan 25, 2012 at 3:22
• This is the right answer. Another confusing wording to look out for: "At least one and at most one" = "exactly one". Commented Oct 15, 2014 at 11:48

if this had been read aloud by the author before publishing it may have been revised to say: "No new vehicle is used until only one remains unused."

• Ah, but that would leave unspecified the matter of exactly what "unused" means. I sense your job doesn't involve writing fleet management rule books! :) Commented Jan 25, 2012 at 2:15

for example, x=0 at all but at most one point in (a,b) means all the x are zeros except at most one point in (a,b) may be non-zero.

• This is even more confusing than the OP's original statement. Commented Oct 15, 2014 at 11:54