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(C) To find the next year when the birthday falls on a Sunday,we calculate the number of odd days. $A$ year has $1$ odd day if it is a normal year ($3

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$1981$

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(C) To find the next year when the birthday falls on a Sunday,we calculate the number of odd days. $A$ year has $1$ odd day if it is a normal year ($365$ days) and $2$ odd days if it is a leap year ($366$ days).From September $6, 1970$ to September $6, 1981$:$1970$ to $1971$: $1$ odd day$1971$ to $1972$: $2$ odd days (leap year)$1972$ to $1973$: $1$ odd day$1973$ to $1974$: $1$ odd day$1974$ to $1975$: $1$ odd day$1975$ to $1976$: $2$ odd days (leap year)$1976$ to $1977$: $1$ odd day$1977$ to $1978$: $1$ odd day$1978$ to $1979$: $1$ odd day$1979$ to $1980$: $2$ odd days (leap year)$1980$ to $1981$: $1$ odd dayTotal odd days = $1+2+1+1+1+2+1+1+1+2+1 = 14$.Since $14$ is divisible by $7$,the remainder is $0$. Therefore,the day of the week remains the same after $14$ odd days.Thus,the birthday will fall on a Sunday again in $1981$.

$A$ girl was born on September $6, 1970$,which happened to be a Sunday. Her birthday would have fallen again on a Sunday in:

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