This puzzle was based on a story problem listed in an academic reading I studied for a math education course. On page 300 in Siegler's Children's Thinking (2nd edition), the following problem is given:

Joe has 23 marbles; he has 7 more than Bill had yesterday before he gave Joe half of his marbles; how many fewer marbles does Bill have today than yesterday?

Yikes. Even though all that is required to solve this problem are very basic addition and subtraction skills, this problem is a bear! Siegler makes the point that it is the un-natural phrasings of math story problems (this one in particular) that tend to make story problems difficult. While story problems can contain similarities to the real world (and thus make it easier to understand the details of the problem), they can also be worded in cumbersome, formal language. In order to solve this problem, your brain has to go through an additional decoding step to translate the problem into something you can make some sense out of. (Specifically, working memory must take on the additional cognitive load of this decoding step, leaving less space for the actual mathematical problem solving.)

Of course, I’m always looking for ideas for logic puzzles, and this seemed like a good (read: devilish) one. While the math in my marbles logic problem doesn't require anything more than addition, subtraction, multiplication, and division, it is very difficult because of the cumbersome language and massive decoding that must take place. It does not need to be solved using any sort of variables or equations (as are used in the detailed solution), but they can help keep things straight.

Many thanks go out to my good friend Niki, who tested the puzzle out for me. She's still speaking to me, thankfully.

 

Solution to Siegler's problem:

Joe today = 23

7 more than Bill yesterday, thus Bill yesterday = 16

Bill gave Joe half of Bill's marbles, thus half of Bill yesterday = 16/2 = 8 (which is the answer to the question).

Joe today = 23, thus Joe yesterday = 23 – 8 = 15

Here's the whole transaction:

Reference: Siegler, R (1991). Children's Thinking, Ed 2. Englewood Cliffs, NJ: Prentice Hall.