Problems of the Month--January 2010

A Look At The Past Decade – The Problems
January 04, 2010

2010 is the start of a new decade, so here are a few New Year's problems.

1. At the start of the last decade everyone was concerned about Y2K... Well, we made it. Y2K was here and gone with no major problems. Interesting thing about the first date of the new millennium, 01/01/00 - when the digits of that date are added, it's the smallest possible sum of any date. What date during the next century, when written in that form, will have the greatest possible sum of its digits?

2. This New Year's date, 01/01/10, has a sum of digits equal to three. Find ten dates with the same sum of digits.

3. How many seconds will occur this millennium (the year 2000 through the year 2999)? Express your answer in scientific notation.

4. New Year's eve is a time when many people make resolutions...
Kaitlyn decided that she would like to read more during 2010, so she made a resolution to read 30 minutes each day. If Kaitlyn reads an average of 1 page every 2 minutes and she finishes her 6th book at the end of her reading session on March 31, 2010, what would be the average number of pages per book for these six books?

5. Nora’s resolution is to get more exercise. She decided that starting with the first full week in 2010, she will do a 45-minute workout four times each week (four days during every seven-day period). This means she will have to exercise four of the days during the week of Jan. 1 through Jan. 7, and then four of the days during the week of Jan. 8 through Jan. 14, and so on. If Nora sticks to her resolution, what is the first possible date on which she could reach a total of 25 hours of exercise for the year?