20 is a composite number. 20 = 1 x 20, 2 x 10, or 4 x 5. Factors of 20: 1, 2, 4, 5, 10, 20. Prime factorization: 20 = 2 x 2 x 5, which can also be written 20 = 2² x 5.

When 20 is a clue in the FIND THE FACTORS puzzles, use either 4 x 5 or 2 x 10. Only one set of those factors will work for any particular puzzle.

Estimating is a very important skill in mathematics, and I have always done well on any homework or test question involving that skill. However, I have never been very good at estimating real life – like how much time it will take me to do something.

Having never blogged before writing this one, I seriously underestimated how much time each puzzle would take me to create and test, and how much time each post would take me to write. Even though I have a large number of level 4, 5, and 6 puzzles already created, I still like to test them all again before I publish them, and that takes time.

Like most people, I work to make a living, and I have only a limited amount of free time each day. There are also other things that I ought to do or want to do that I haven’t given sufficient time in the last two months.

Because I underestimated my time and overestimated other things, I’ve decided to downsize and only publish posts on Mondays. Therefore there will not be any new puzzles today. Here is the easiest puzzle and the hardest puzzle from last week:

To solve them, place the numbers 1- 12 in the top row and again in the first column so that those numbers are the factors of the given clues. Click 12 Factors 2013-12-26 to see the solutions for all of the puzzles from last Thursday. Excel or similar spreadsheet program is needed to open the file. This Monday I will publish more 12 Factor puzzles followed by 10 factor puzzles the following week.

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There are much worse things to underestimate:

- Geologists report that risks of big earthquakes may be underestimated (phys.org)
- ‘IMF Admits it Underestimated the Fiscal Multiplier’ (economistsview.typepad.com)

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