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The Hours Two Ends ShareAll notes

The gap

What a gap costs

One hour of overlap lost for every hour of gap, until there is nothing left to lose.

Part one

9 notes in this part

The One Law This Whole Record Rests On

Two working days of the same length lose exactly one hour of overlap for every hour of gap. Almost every figure here follows from that sentence.

Reference

What Two Ends Share At No Gap

A gap of zero leaves all eight hours, four before the middle of the day and four after. The only even split in the record.

Reference

Three, Four And Five Hours Apart

The middle of the range, where half the working day survives and two reasonable people reach opposite conclusions about the same number.

Analysis

Where The Arrangement Stops Existing

At a gap of eight hours two ordinary days share nothing, and at twelve they still share nothing. Ten of the twenty-five gaps are in this state.

Reference

Which Half Of The Overlap You Get

Every gap splits its shared hours into a part before the middle of the day and a part after. One side empties completely before the other loses anything.

Reference

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.

Reference

Neither The Best Nor The Worst Case

Across the fifteen gaps that leave anything, the median shared time is four hours. The mean over all twenty-five would describe no arrangement at all.

Analysis