Information Work: Numbers and Solving Problems

### Information Work: Numbers and Solving Problems

Division of space and other issues of great importance in previous eras puzzle most people today. Indeed puzzles pose difficulties. It is easy to become blocked - unable to reason. The idea of this material is to organize a series of puzzling items to support learning activity. (To become qualified for information work, one must get used to overcoming blocks.) One way to describe learning flexibility is thinking outside the box . Puzzles were the domain of an acknowledged master at creating them Sam Loyd - "Loyd produced over 10 000 puzzles in his lifetime many involving sophisticated mathematical ideas." To see his work Begin Here and go to links it describes. A sample is the Horse and Rider puzzle. (Its Solution is available.)
 Ascher, M. Ethnomathematics Kasner/Newman Mathematics & Imagination Tetrahedron - Four-Sided Block Big - Large Number Sizes
The organizing principle behind blocks has two parts. First, there's something interesting to learn from a block. As a spiritual song puts it, "Lord, don't take away my stumbling blocks. Just give me the power to climb." Second, an act of will is the essential step in climbing. The act can start by just asking a question such as what does that symbol mean? Two examples are the:
number 8 in the expression 108, an Exponent; and,
exclamation point in 7!, the Factorial.

Using signs and symbols to express ideas is learnable ... if you want to do it.
If you think you can do a thing or think you can't do a thing, you're right. - Henry Ford; Human beings can alter their lives by altering their attitudes of mind. - William James; You may have a fresh start any moment you choose, for this thing we call 'failure' is not the falling down, but the staying down. - Mary Pickford
The thought that led to products - quarrying and fitting stones into walls; things about curves, lines and closeness - endure today. More to the point, we have ability. A try followed by an assist is one way to learn. Many solutions are a click away in other files, such as posted images and book sources.
[A question related to computing (first asked me by Merwyn Sommer).]

### Find what should follow 24 in: 10, 11, 12, 13, 14, 15, 16, 17, 20, 22, 24, __?

This question is usually seen as fairly difficult. But the reason it is so has to do with our inability to think outside the box, i.e., our ordinary mode. Even with a hint (italicized words above), people tend to limit their range of alternatives - in other words, create blocks.

What makes it difficult for most people to answer this?