February ’16 Brain Teasers

1. What can you hold in your left hand, but not your right hand? (Multiple answers?)
2.  In the US, 5/2 means May 2, but in England it means Feb 5 (they put the day first).  How many days each year have the same abbreviations in both countries?
3. What is the next combination of letters and numbers in this pattern?  A1Z26, B3Y24, C5X22, ____
4. Find the smallest of 5 consecutive integers whose sum is 100.
5. Find any value of t that makes 19/t + 5/t a whole number.  (Mini Bonus:  Can you find all values of t that work?)
6. At what time is the sum of the digits on a digital clock the greatest?
7. The transistor was invented in a year close to the middle of the 20^th century. The tens’ digit of the year is 4 times the thousands’ digit and one-half of the ones’ digit.  In what year was it invented?
8. Two 5 x 5 squares overlap to form a 5 x 7 rectangle. What is the area of the region in which the two squares overlap?
9. What fraction of the small squares on a chessboard are covered (occupied) by playing pieces at the start of the game?
10. Eric’s school system has 9000 pupils and a teacher-pupil ratio of 1:30. They feel this is too high, and want to reduce it to 1:25.  How many more or fewer teachers are needed to achieve this goal?
Exploration/Mini Research?  We have another 5-Monday-month this month – and it’s February!!  This has got to be rare! It has to be leap year to have 5 of any day in February, but Mondays?  HOW RARE IS THIS?
(I only know this answer vaguely, and I don’t think it’s exact.  I suspect I’m just wanting someone to Google it for us and fill us in.  :-))

 Submit Answers!  There are NO tests and the answers are NOT graded, so lighten up!  If you want to submit  your answers to any or all of these, PLEASE feel free to do so!!  

You can always do this 3 ways:  1)  Use the Leave A Reply section below (though I may not make it public until after the deadline);   2) reply to (or contact) me directly by e-mail or by replying to any Weekly Sharing; or 3) by using the Contact Form link.   

Reminder:  Official deadline for  ALL BT submissions in February is noon, Thursday, Feb 25. (Late submissions accepted if Answer Sheet hasn’t been prepared/posted, but no promises.) Solutions will likely appear on Monday, Mar 7.