The term sometimes used in the Shire for the number that would more normally be called 'one hundred and ten'. It was seen particularly in references to Bilbo Baggins' 'eleventy-first' birthday (or, more naturally, his hundred and eleventh), on which he disappeared at his Birthday Party and left the Shire.
The use of 'eleventy' by the Shire-hobbits reflects the presence in Old English of the word endleofantig (from enleofan, 'eleven') which, if it had survived into modern usage, would certainly have become 'eleventy'. This is one of several instances where Tolkien gives his Hobbits modernised Old English names for everyday things - smial and mathom are other prominent examples. This relationship to Old English suggests that a similar tradition existed in Rohan, whose people shared a linguistic heritage with the Hobbits.
The existence in archaic English of old words equivalent to 'eleventy' (and 'twelfty') imply the survival of an ancient duodecimal (base twelve) numbering system among the Anglo-Saxons. Fragments of this even remain in modern English (for example, the fact that we use special words for 'eleven' and 'twelve' rather than following the pattern of the other 'teens' with words something like 'oneteen' or 'twoteen'). More notably, we still have special names for the number twelve (a 'dozen') and twelve twelves (a 'gross'), and this indirect connection between 'eleventy' and 'gross' perhaps inspired Bilbo's insulting reference to his 144 guests as one Gross in his Farewell Speech.
There was a linguistic connection between the Shire-hobbits and the Rohirrim, due to their shared ancient history in the Vales of Anduin. This is emphasised by the use of Old English to represent the language of Rohan, and the fact that 'eleventy' comes from Old English endleofantig implies that the Rohirrim likely had a comparable concept.
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