A father has seven children. Each child was born on a different day of the week, starting from Monday through Sunday. The sum of their ages is equal to the father's age. The youngest child is 1 year old, and the oldest child is 7 years old. On what day of the week was the father born?
The father was born on a Wednesday.

Here's the reasoning:

1. We know the ages of all seven children: 1, 2, 3, 4, 5, 6, and 7 years old.
2. To find the father's age, we add up the ages of all his children: 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28 years old.
3. Now, let's find out how many weeks are in 28 years: 28 years * 52 weeks/year = 1456 weeks.
4. Since there are 7 days in a week, we can divide the total number of days in 28 years by 7: (28 * 365) / 7 = 1460.
5. Now, let's find the remainder when dividing 1460 by 7: 1460 % 7 = 3.
6. Since there are three extra days beyond a complete number of weeks, we can count forward from Monday (the day the youngest child was born) to determine the father's birth day:
   - Monday + 1 day = Tuesday
   - Tuesday + 1 day = Wednesday
   - Wednesday + 1 day = Thursday

So, the father was born on a Wednesday.