It was Sunday on Jan 1, 2006. What was the day of the week Jan 1, 2010?

Question

A party host says to two strangers Abby and Barry, “Each of you knows which day of the week you were born on, but not the day of the week the other was born on. But I can tell you that Barry was not born on Monday, and you were born one day apart (on consecutive days).”

He then asks Abby and Barry alternately if either can deduce the day of the week the other person was born on.

Abby: “No.”
Barry: “No.”
Abby: “No.”
Barry: “No.”
Abby: “No.”
Barry: “Yes!”

What day of the week was Abby born on? Can you deduce the day of the week for Barry?

Answer 1

If it's Sunday on January 1st 2006 then on January 1st 2010 it's Friday.

Jan 2006 - Jan 2007 = 365 days
Jan 2007 - Jan 2008 = 365 days
Jan 2008 - Jan 2009 = 366 days( It's a leap year )
Jan 2009 - Jan 2010 = 365 days.
Total days = 1461 days.

1456 is divisible by 7 (There are 7 days in a week ) so the remainder is +5 for 1461. Which implies Sunday + 5 days = Friday.

Answer 2

Taking into account that every four years, there is a leap year. Every normal new year Jan1 moves one day within the week, while for the leap year, Jan 1 moves two days within the week. Therefore, Jan 1 will move to say 3 + 2 days. Then, Jan1 in 2010 will be FRIDAY.