Natural Blogarithms

The four numbers A, B, A+B and A-B are all prime.  The sum of these four numbers is
A) EvenB) Divisible by 3C) Divisible by 5D) Divisible by 7E) Prime
Source: 2002 AMC 10/12B #15

I love these kinds of puzzles because there is only one solution but there are several ways to get there.  It’s at least as interesting to hear the different approaches as it is to solve it.
Here was the puzzle posted last week:
Mr. Jones has eight children of different ages.  On a family trip his [...]

   Mr. Jones has eight children of different ages.  On a family trip his oldest child, who is 9, spots a license plate with 4-digit number in which each of two digits appears two times. 
  “Look, daddy!” she exclaims. “That number is evenly divisible by the age of each of us kids!”
  “That’s [...]

Two days ago, I posted this simple little number puzzle. Quite a few folks came up with the answer below.  One of the interesting questions you can ask is whether that solution is unique.
 
Clearly there are two lines of symmetry in the original problem so by reflection alone we come up with a total [...]

I’m not keeping very good track of how many of these kind of puzzles I’m posting, so we’ll just say this is the 6th.
Problem: Place the digits 1 through 8 in the circles below such that no two adjacent circles contain consecutive digits.

 
Update: I was missing a couple of lines.  The picture is now [...]

I know some of you who read this blog also read 360 but the sequence posted there today was too good to not pass along:
Puzzle:  Identify the next term in the sequence
1, 11, 21, 1211, 111221, 312211, 13112221, . . .

[HINT: Read the digits aloud.  The sequence is aural/visual and not numeric.]
I’ll post the answer [...]

I’m embarrassed by the fact that I have 3 weeks of Twitter updates cluttering the first page of this blog.  That means, that I’ve gone without blogging for at least two weeks.  I was trying to get on a roll with the number puzzles.  I have a backlog of some interesting links and topics in [...]

Sally has five red cards numbered 1 through 5 and four blue cards numbered 3 through 6. She stacks the cards so that the colors alternate and so that the number on each red card divides evenly into the number on each neighboring blue card. What is the sum of the numbers on the middle [...]

Form a number from the digits 0 to 9 such that the first digit is divisible by one, the first two digits form a number that is divisible by two, the first three digits form a number that is divisible by three, and so forth.
I’ll post my solution in a day or two.
HT: QYV [...]

A couple of days ago, I posted the following puzzle:
There is a ten digit number where the leftmost digit is also the number of zeros in  the number, the second leftmost digit is the number of ones and so forth until the last digit (or rightmost digit) is the number of nines in that number. [...]