Sorry, no cool number days this week.

But, as promised on June 23, we will look at how much longer Half-back days are going to last this century.  Recall from the calculations back then, the way to find the DAY when the MONTH and YEAR are known is with the simple formula

                d = 2y – m   OR   d + m= 2y

There are limits on year, month, and day values:

                0 <= y <= 99  (only 100 years in a century!)

                1 <= m <= 12  (only 12 months in a year!)

                And day limits vary by month

                1 <= d <= 28 or 29 for February

                1 <= d <=30 for April, June, September, and November

                1 <= d <= 31 for January, March, May, July, August, October, and December

 

Start with January.

m = 1; d <=31; and d + m = 2y, so

31 + 1 <= d + m =2y

32 <= 2y

16 <= y

So, 1/31/16 (up 30 and back 15) is the last January half-back day of the century.

 

And look at February.

m = 2; d<=29; and d + 2m = 2y

29 + 2 <= d + m = 2y

31 <= 2y

15.5 <=y

Month and day have to both be even, for the 2y to work!

2/28/15 is the last February half-back day until 2/2/2100… wrap your head around that one!

 

We will figure out the rest of the months on October 6.  There will be a surprise because February’s 28 days masks a pattern.