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When you visit your favorite restaurant can you smell the food even before walking inside? Can you feel the difference between the soft fur of a puppy and the cold wet nose? If a bright red bird swoops by, can you identify what kind of bird it is just by color? Should you pay to use your senses?

That is the premise for A Case of Sense; a new book by author Songju Ma Daemicke illustrated by Shennen Bersani. The book opens with a young boy playing outside, and greedy Fu Wang has cooked wonderful Chinese dishes with the smells wafting throughout town. He announces that the townspeople must pay for the smells and when they don’t he takes everyone to court! The judge has a clever way to deal with the case and readers might use a little logical reasoning to figure out the puzzle.

Saturday, Songju will be signing at the ISLMA conference in Tinley Park, IL from 2pm-4pm. In celebration, we have a fun little puzzle in logic and sight that might keep kids coloring for a little while!

Get out the markers or the crayons and color in the missing spaces. Remember that all the colors will be rows, columns, and squares of 9 without repeating!

Download the printable PDF version! 

Download the answers here!

I want to tell you about the marvelous things I have been doing and reading..... but all I seem to do is Sudoku puzzles.  And I'm a mathphobe, too.  Hmmmmmm.

I have made a resolution.  I will do NO Sudoku puzzles before bedtime.  I will do no puzzles AT ALL before bedtime.  If I find myself watching television and I need something to do with my hands, I will make paper beads, exercise during the commercials, crochet, take notes for story ideas, fold wash - ANYTHING BUT PUZZLES.

A puzzle or two when I am tucked up in bed - ok.  That's acceptable.  But NO going to bed early just to do puzzles.  And I would.  If I could.  Anyway, that's one reason this blog has been skimpy lately.  Sudoku.

There are tons of books on the market that instruct us on how to make more money, spend less of it, and where to stash what we haven’t spent. Like many, spending and saving has more than one meaning for me. We all must decide how much, where and when money comes into the picture and what we mean by money.

Monetary worth is often measured by $ saved in bank accounts. There are other measures as well, and other types of banks. A person can save herself from a variety of situations, circumstances, and disasters. She can save her energies for special occasions, and so on. Euphemisms abound regarding saving.

In today’s catch-as-catch-can world of finance, saving money in banks is getting harder to do. The meaning of “saving money” has shifted to refer as much to buying for less as is does “squirrelling away cash.” For those who’re trying to make it in the publishing business, demands on the wallet is as constant as those for any other self-employed entrepreneur. Most of us have a “day” job to make it through.

Ingenious writers and other artists work smarter to make gains. Payment for a job doesn’t have to go in the bank. For many beginners, and those who have a few sales under their belts, barter has become a mainstay of payment.

An artist, in one example, has her eye on a specific gallery to display her work. Such displays cost the artist money. The gallery has no Facebook account. She offers to trade her knowledge of the web for display space in the gallery. Each side gets rewarded for the deal.

At the same time, she can offer to advertise the gallery on her own website, FB account, and other outlets, for framing her work in the gallery. The gallery owner spends nothing for the advertising and minimal cost for the framing he performs already. The artist gets everything she wants: exposure in a smaller, but good gallery and free framing.

The same type of arrangement can be used by a writer. The writer goes to a small company that has something she wants. She offers to do some work for them in exchange for whatever product the company provides. They strike a bargain and do a short contract for the job; she will write two professional short (form) business letters for the company; they give her the product—let’s say wheel alignment on her car.

Use the cashless jobs to build your resume. If you know of an organization that has decided to create a newsletter for its members and friends, offer to assist or to do it for them. The project gives you practice in something you might not have done before. It could also land you a job writing the newsletter on a regular basis. At that point you could talk compensation. If you don’t get paid, you still have another skill credit and client on your resume.

What if your child’s school needs help creating a small play for the fourth graders? Are you able to stretch your abilities to help with that project? Have you ever tried to write a children’s play? You might be very good at it, and there are opportunities for sales of such plays on the market. Practice on the school’s project, grab a resume credit and see what the future holds later.

How about developing the types of puzzles, mazes, and games that fascinate

By Jason Rosenhouse

Among mathematicians, it is always a happy moment when a long-standing problem is suddenly solved. The year 2012 started with such a moment, when an Irish mathematician named Gary McGuire announced a solution to the minimal-clue problem for Sudoku puzzles.

You have seen Sudoku puzzles, no doubt, since they are nowadays ubiquitous in newspapers and magazines. They look like this:

Your task is to fill in the vacant cells with the digits from 1-9 in such a way that each row, column and three by three block contains each digit exactly once. In a proper puzzle, the starting clues are such as to guarantee there is only one way of completing the square.

This particular puzzle has just seventeen starting clues. It had long been believed that seventeen was the minimum number for any proper puzzle. Mathematician Gordon Royle maintains an online database which currently contains close to fifty thousand puzzles with seventeen starting clues (in fact, the puzzle above is adapted from one of the puzzles in that list). However, despite extensive computer searching, no example of a puzzle with sixteen or fewer clues had ever been found.

The problem was that an exhaustive computer search seemed impossible. There were simply too many possibilities to consider. Even using the best modern hardware, and employing the most efficient search techniques known, hundreds of thousands of years would have been required.

Pure mathematics likewise provided little assistance. It is easy to see that seven clues must be insufficient. With seven starting clues there would be at least two digits that were not represented at the start of the puzzle. To be concrete, let us say that there were no 1s or 2s in the starting grid. Then, in any completion of the starting grid it would be possible simply to change all the 1s to 2s, and all the 2s to 1s, to produce a second valid solution to the puzzle. After making this observation, however, it is already unclear how to continue. Even a simple argument proving the insufficiency of eight clues has proven elusive.

McGuire’s solution requires a combination of mathematics and computer science. To reduce the time required for an exhaustive search he employed the idea of an “unavoidable set.” Consider the shaded cells in this Sudoku square:

Now imagine a starting puzzle having this square for a solution. Can you see why we would need to have at least one starting clue in one of those shaded cells? The reason is that if we did not, then we would be able to toggle the digits in those cells to produce a second solution to the same puzzle. In fact, this particular Sudoku square has a lot of similar unavoidable sets; in general some squares will have more than others, and of different types. Part of McGuire’s solution involved finding a large collection of certain types of unavoidable sets in every Sudoku square under consideration.

Finding these unavoidable sets permits a dramatic reduction in the size of the space that must be searched. Rather than searching through every sixteen-clue subset of a given Sudoku square, desperately looking for one that is actually a proper puzzle, we need only consider sets of sixteen starting clues containing at l

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By Jason Rosenhouse

A recent satirical essay in the Huffington Post reports that congressional Republicans are trying to legislate the value of pi. Fearing that the complexity of modern geometry is hurting America’s performance on international measures of mathematical knowledge, they have decreed that from now on pi shall be equal to three. It is a sad commentary on American culture that you must read slowly and carefully to be certain the essay is just satire.

It has been wisely observed that reality is that which, when you stop believing in it, doesn’t go away. Scientists are especially aware of this, since it is sometimes their sad duty to inform people of truths they would prefer not to accept. Evolution cannot be made to go away by folding you arms and shaking your head, and the planet is warming precipitously regardless of what certain business interests claim to believe. Likewise, the value of pi is what it is, no matter what a legislative body might think.

That value, of course, is found by dividing the circumference of a circle by its diameter. Except that if you take an actual circular object and apply your measuring devices to it you will obtain only a crude approximation to pi. The actual value is an irrational number, meaning that it is a decimal that goes on forever without repeating itself. One of my middle school math teachers once told me that it is just crazy for a number to behave in such a fashion, and that is why it is said to be irrational. Since I rather liked that explanation, you can imagine my disappointment at learning it was not correct.

In this context, the word “irrational” really just means “not a ratio.” More specifically, it is not a ratio of two integers. You see, if you divide one integer by another there are only two things that can happen. Either the process ends or it goes on forever by repeating a pattern. For example, if you divide one by four you get .25, while if you divide one by three you get .3333… . That these are the only possibilities can be proved with some elementary number theory, but I shall spare you the details of how that is done. That aside, our conclusion is that since pi never ends and never repeats, it cannot be written as one integer divided by another.

Which might make you wonder how anyone evaluated pi in the first place. If the number is defined geometrically, but we cannot hope to measure real circles with sufficient accuracy, then why do we constantly hear about computers evaluating its first umpteen million digits? The answer is that we are not forced to define pi in terms of circles. The number arises in other contexts, notably trigonometry. By coupling certain facts about right triangles with techniques drawn from calculus, you can express pi as the sum of a certain infinite series. That is, you can find a never-ending list of numbers that gets smaller and smaller and smaller, with the property that the more of the numbers you sum the better your approximation to pi. Very cool stuff.

Of course, I’m sure we all know that pi is a little bit larger than three. This means that any circle is just over three times larger around than it is across. The failure of most people to be able to visualize this leads to a classic bar bet. Take any tall, thin, drinking glass, the kind with a long stem, and ask the person sitting nearest you if its height is greater than its circumference. When he answers that it is, bet him that he is wrong. Optically, most such glasses appear to be much taller than they are fat, but unless your specimen is very tall and very thin you will win the bet every time. The circumference is more than three times larger than the diameter at the top of the glass. A vessel so proportioned that this length is nonetheless smal