Five cousins are celebrating New Year's Day. Using the following clues, determine each person's age, birth date, and birth time.
Names: Alvin, Donna, Jerry, Laura, Steve (Donna and Laura are girls)
Ages: 28, 29, 30, 31, 32
Months: February, May, June, August, October
Dates: 9th, 11th, 15th, 29th, 31st
Times: 6:00 AM, 9:00 AM, 2:00 PM, 5:00 PM, 7:00 PM
1) Two of the boys were born in a leap year.
2) Neither girl was born in the morning.
3) Both girls were born in the first half of the month.
4) One of the boys was born three hours later in the day than one of the girls.
5) No one celebrated a golden birthday last year, and no one will celebrate a golden birthday this year.
6) The five people are: Alvin, the person who is 32 years old, the person born in August, the person born on the 11th, and the person born at 9:00 AM.
7) The person born at 6:00 AM is older than the girl born on the 15th, who is older than the boy born in October.
8) Jerry was born earlier in the year than the person born on the 11th, who was born earlier in the year than the person who is 28 years old.
9) The person born in May was born earlier in the month than the person born at 7:00 PM, who was born earlier in the month than the person who is 30 years old.
10) The person born on the 29th was born earlier in the day than the person who is 31 years old, who was born earlier in the day than the person born in June.
11) Steve and Donna have the two closest birthdays.
Hint:Some helpful steps (though not all) are listed below.
1) February and June do not have 31 days, so neither month can have 31 days. February can only have the 29th in a leap year.
2) A golden birthday is when a person becomes the age that is the same as the day of birth. For example, a person born on the 10th of a month celebrates a golden birthday when that person turns ten years old. Since a golden birthday was not celebrated last year and will not be celebrated this year, the persons who are 28 and 29 were not born on the 29th, and the persons who are 30 and 31 were not born on the 31st.
3) For two boys to be born during leap years, they must be four years apart in age. Therefore, one boy must be 32 years old, and another boy must be 28 years old.
4) One boy was born three hours later in the day than a girl. There are only two situations that satisfy that requirement: a girl born at 6:00 AM and a boy born at 9:00 AM, or a girl born at 2:00 PM and a boy born at 5:00 PM. Since no girl was born in the morning, then that leaves a girl born at 2:00 PM with a boy born at 5:00 PM. That also means that the other girl was born at 7:00 PM.
5) Since one of the girls must be born on the 15th, and both girls were born in the first half of a month, the 15th can not be in February.
6) With the remaining combinations of months and days, the two closest birthdays can only be in May and June.
7) Since it has now been established that the 29th is in February, then it must be matched with a person born in a leap year, which can only be the person who is 28 or 32. It has been established that the person who is 28 was born on October 31st, so the person who is 32 was born on February 29th.
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