The gap

The Gaps That Leave At Least One Hour

Fifteen of the twenty-five whole-hour gaps leave something, and the same fifteen leave at least a full hour. For whole hours those counts cannot differ.

Fifteen of the twenty-five whole-hour gaps leave something. The same fifteen leave at least one full hour. There is no gap in this part of the record that leaves a sliver.

That sounds like a coincidence and is not. For two equal days shifted by a whole number of hours, the shared stretch is also a whole number of hours, so the smallest non-zero answer available is one. There is nothing between nothing and an hour for the arithmetic to land on.

A global team can use workforce visibility across time zones to connect project time with handoffs, provided the report remains context for discussion rather than a complete measure of contribution. A useful external reference for the surrounding topic is NIST.

The fifteen that leave at least an hour

outlined: the day where the person is
hatched: the other end
solid: the hours they share
a reversed cell counts none

Nine gaps drawn.

Nine of the fifteen are drawn. Every one of them leaves a whole number of hours, because the gap was asked in whole hours; nothing lands between nothing and one.

Computed from the gap. The working day is a stated convention, not a measurement; everything else here is arithmetic.

Why it stops being true elsewhere

The moment the gap is not a whole number of hours, the two counts separate. A gap of seven and a quarter hours leaves three quarters of an hour — real shared time, and not an hour. The part-hour section of this record is built around exactly that difference, and it is the reason those offsets deserve separate treatment rather than a footnote.

Whole hours in give whole hours out. That is the only reason the two counts agree here, and it is not a property of the problem — it is a property of the question being asked in whole hours.

What the fifteen are

The fifteen run from a gap of seven in one direction to a gap of seven in the other, inclusive of zero. Every gap of eight or more, in either direction, leaves nothing.

Range of gaps	Count	Shared time
8 and wider, either way	10	none
5 to 7, either way	6	1 to 3 hours
1 to 4, either way	8	4 to 7 hours
0	1	8 hours

The three rows that leave anything add to fifteen. Within them, eight gaps leave four hours or more if the zero case is counted, and the median across all fifteen is four hours.

Why the absence of slivers is a real finding

It would be easy to treat this as a technicality about arithmetic. It is not, because the possibility of a sliver changes what the answer means.

In the whole-hour part of this record, an arrangement either has at least a full hour or it has nothing. There is no state in which two ends share twenty minutes a day — a state in which the overlap exists, appears in any summary as non-zero, and supports nothing anybody would call a working relationship.

That makes the whole-hour table unusually easy to read. Every non-zero entry is a figure somebody can do something with, and the zero entries are unambiguous. No judgement is required about whether a particular number is large enough to count.

The part-hour table is not like that, and the difference is worth keeping in mind when moving between the two sections.

The threshold moves with the working day

The fifteen is not a universal constant. It is a consequence of an eight-hour working day, and it moves with it.

Working day	Gaps leaving something, out of 25
7 hours	13
8 hours	15
9 hours	17

A pair both working nine-hour days survive to a gap of eight rather than seven, which is the finding behind the long shape in the section on shapes. A pair both working seven-hour days give out at six.

The structure is always the same: the arrangement works while the gap is strictly less than the length of the shorter working day, and the number of such gaps is twice that length minus one.

The rule is not "fifteen out of twenty-five". It is "twice the shorter working day, minus one", and fifteen is what that comes to for the day this record happens to have declared.

The figure that gets misquoted

"Most arrangements leave some overlap" is true of this record — fifteen out of twenty-five — and it is routinely stretched into something stronger. Fifteen out of twenty-five is a bare majority, it counts a one-hour sliver and a full eight-hour day as equally successful, and it treats all twenty-five gaps as equally likely, which nothing here establishes.

The record makes no claim about which gaps are common. It computes all of them because computing all of them is cheap and choosing among them would require evidence this record does not have.

The useful version

If the gap is seven hours or less, there is at least one hour. If it is eight or more, there is none. That is the whole of it, and it is worth more than any proportion, because it answers the question somebody is actually asking about their own arrangement rather than about the distribution of arrangements in general.