Headington District did in fact, span the Oxfordshire and Buckinghamshire boundary, but was primarily in Oxfordshire.

Mary's father was Thomas Sykes, a labourer.
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Mary appears in 1871 living at Buckingham, Buckinghamshire, England with her daughter Emma:
Mary Ann Knibbs abt 1821 Diddington Oxfordshire Head Buckingham Buckinghamshire
Emma Knibbs abt 1859 Diddington Oxfordshire Daughter Buckingham Buckinghamshire

Her husband Francis wasn't with her, so it is presumed that he died before 1871.
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Mary appears in the 1881 census as Mary A Knibbs, widowed, living at Bone Hill, Buckingham, Buckinghamshire, England
Mary A. KNIBBS Lodger (Head) W Female 60 Deddington, Oxford, England Charwoman

I see in the census that living next door to Mary there was a man named Joseph North, aged 73, a widower with the trade of Hay Tier, although he's identified in the census as "unable to work". I wonder, was he the owner of the house she was lodging in, and was she perhaps looking after him? - was the William North she married his brother? All pure speculation on my part.
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The Bucks Herald on 26 August 1882 reported a marriage at Buckingham on 20th August 1882 between William North and Mrs Emma Knibbs. The GRO has this marriage listed for Mary Ann Knibbs. I believe the GRO would be the more accurate source of information, so I presume this was a third marriage for Mary Ann Sykes.
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It's interesting to note also that Mary's son John Francis Knibbs married a girl named Cecelia North - any relation to Mary's third husband perhaps?
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There's no sign of Mary living at Buckingham in the 1901 census, but there's a William North, aged 82, occupation Hay Tier, so I wonder if this William North could be Mary's widowed husband?