SOLUTION: Mom turned 90 on Friday, June 2, 2006. On what day of the week was she born? A.Sunday B.Monday C.Thursday D.Friday E.Saturday

Question 265931: Mom turned 90 on Friday, June 2, 2006. On what day of the week was she born?
A.Sunday B.Monday C.Thursday D.Friday E.Saturday

Answer by CharlesG2(834) (Show Source): You can put this solution on YOUR website!
Mom turned 90 on Friday, June 2, 2006. On what day of the week was she born?
A.Sunday B.Monday C.Thursday D.Friday E.Saturday
2006 - 90 = 1916
so we are figuring out what day of the week June 2, 1916 was on
1900 is not a leap year, 2000 is a leap year, and 1916 was a leap year
(see: http://quasar.as.utexas.edu/BillInfo/doomsday.html , John Horton Conway's method based on doomsdays (days that occur on the same day of the week)
(see also: http://en.wikipedia.org/wiki/Doomsday_rule)
"This algorithm involves treating days of the week like numbers mod 7, so John Conway suggests thinking of the days of the week as Noneday, Oneday, Twosday, Treblesday, Foursday, Fiveday, and Six-a-day."
"We first take the anchor day for the century. For the purposes of the Doomsday rule, a century starts with a 00 year and ends with a 99 year. The following table shows the anchor day of centuries 1800�1899, 1900�1999, 2000�2099 and 2100�2199.
Century Anchor day Mnemonic Index (day of week)
1800�1899 Friday - 5 (Fiveday)
1900�1999 Wednesday We-in-dis-day
(most living people were born in that century) 3 (Treblesday)
2000�2099 Tuesday Y-Tue-K or Twos-day
(Y2K was at the head of this century) 2 (Twosday)
2100�2199 Sunday 20-One-day is Sunday
(2100 is the start of the next century) 0 (Noneday)
Since in the Gregorian calendar there are 146097 days, or exactly 20871 seven-day weeks, in 400 years, the anchor day repeats every four centuries. For example, the anchor day of 1700�1799 is the same as the anchor day of 2100�2199, i.e. Sunday."
"Part 2-What is Doomsday for any year of this century?
The next and hardest part of the trick (because it requires a small amount of calculation) is to determine Doomsday for the year in question. Here's how to do it.
If the year is 19xx, divide xx by 12 to get a quotient Q and a remainder R;
Divide the remainder R by 4 to get another quotient S (forget the new remainder, it is not used).
Add Q, R and S together, and count that many days starting from Wednesday (which is the special Doomsday that applies to this century). This gives you the Doomsday for the year 19xx. From this point on, just use Part 1.
Example: This year is 1997. 97/12 = 8 remainder 1 so Q=8, R=1 and S=0. Nine days from Wednesday is a Friday, so in 1997, Doomsday is Friday (which we already said).
Example: On what day of the week did D-Day, June 6, 1944, fall? Well, 44/12 = 3 remainder 8, and 8/4 = 2 with remainder 0 which we forget. 3+8+2=13, and counting 13 days from Wednesday is the same as counting -1 day, so Doomsday for 1944 is a Tuesday. Since 6/6 (June 6) is June's magic day, we now know that June 6, 1944 was a Tuesday."
"4/4, 6/6, 8/8, 10/10 and 12/12 always fall on the same day of the week (Doomsday) in any year."
1916 --> divide 16 by 12 to get a quotient Q and a remainder R
Q=1, R=4
Divide R by 4 to get another quotient S --> R/4 = 4/4 = 1 = S
add Q + R + S --> 1 + 4 + 1 = 6
add 6 days to Wednesday --> Tuesday (doomsday for 1916 is a Tuesday)
2006 --> divide 6 by 12 to get Q and R
Q=0, R=6
divide R by 4 to get S --> S=1
Q+R+S = 0 + 6 + 1 = 7
add 7 days to Tuesday --> Tuesday (doomsday for 2006 is also a Tuesday)
June 6, 1916 is a Tuesday and June 6, 2006 is also a Tuesday
therefore June 2, 1916 is a Friday (which was answer D)

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