The middle digit
An interesting pattern involving the middle digit appears in the square of numbers whose digits are all 1's (1^{2}, 11^{2}, 111^{2}, 1111^{2}, etc.). How does the number of 1's relate to the middle digit of the squared number? How does the number of 1's relate to the number of digits of the squared number?
(Source: Mathematics Teaching in the Middle School, SepOct1994)
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