Brain Teasers 15-12

Added 8/24:
5.  Find a three-digit perfect cube whose digits add to a perfect square.  (Hint: there aren’t many possibilities.)
6. (Have I done this one before?)  What are the next three letters in this common sequence:  O, T, T, F, F, S, S, __, __, __ ?
7. (For Math Nerds?)  A “20 inch” bicycle has wheels with a radius of 10 inches.  How many revolutions (roughly) do the wheels make in a mile ride?

 
1.  Old MacDonald had some hens and some rabbits.  Together, these animals have eight heads and twenty-two feet.  How many of each did Farmer Mac have?
2.  Al, Bob, Carl, and Dave were standing in line.  Dave was not first.  Bob was between Al & Carl.  Al was between Dave and Bob.  In what order were they standing in line?
3.  You  lost your place in the book when you dropped it on the floor, but for some reason, you remembered that the product of the pages is 16,002.  (Yeah, I know!  Just play along.  :-))  What are the page numbers?
4.  Pick any two-digit prime number.  It turns out the the number on one side or the other of the prime will be divisible by 6.  Why?

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.   Your anonymity is protected for all formats (but only until submission deadline for the Leave a Reply format. )

Reminder:  Official deadline for these and ALL BT submissions in  August is noon Thursday, Aug 27. (Late submissions accepted if Answer Sheet hasn’t been prepared, but no promises.)