How Many Squares On A Checkerboard

Weigand: It's Donald Duck revisited

Even while Congress furiously debates whether to raise the national debt ceiling by August, with disaster predicted by some if we do, and by others if we don't, and both sides probably right, many citizens still find it hard believing that the nation is in crisis.

Not the phony kind, but one comparable to World War II or the Great Depression.

Though millions have lived productive lives in ignorance of the treacherous nature of mathematical progressions, these are nonetheless real. A Donald Duck comic book issued back in the days when funnies were only a dime illustrates the dangers of our times.

Donald, though himself of modest means, had a fabulously rich uncle, Scrooge McDuck. Stories often related Scrooge's miserly struggle to hoard every dime of his billions while wringing additional nickels out of Donald. But one time the tables turned dramatically, for reasons that have everything to do with current economics.

Once Donald offered to trade his house, worth several thousand dollars, to "Unca" Scrooge for a checkerboard covered with pennies, subject only to the condition that each square double the amount of the preceding one. Square one had one penny, square two got two, and so on through 64 squares.

Penny-pinching Scrooge leaped at the seeming bargain, realizing only too late that he had agreed to pay his nephew more money than existed in the entire world.

You see, multiplying a penny raises it to a little over a dollar after the first file. As the man who fell off the top of the Empire State building said as he neared the first floor, "So far, so good."

But there are seven more files on a checker board. The last square on the second file has over $300 stacked on it, and by line eight the amount is almost beyond calculation. Plus it all has to be added together.

In his happy comic-book world, Donald forgave the debt and Scrooge kept his fortune.

Unfortunately for us, Americans don't dwell inside a comic strip, and neither does China or any other owner of our debt.

That debt, "only" $1 trillion in 1981, is now $14 trillion and rising. Until now, Washington has disguised impending disaster by cranking up the printing presses and "paying" its most urgent creditors with paper and rosy predictions of the future. The scrip's value has shrunk steadily, but people have gone on accepting it because the process has been slow. But today, despite decades of bland governmental reassurances, it looks like it's about to speed up.

How many squares in a checkerboard? Mrs. Dorer's Explorers

Today we tried to figure out how many squares are in a checkerboard. Most people only counted the little squares, which are 1x1 squares. They forgot about the 2x2 's and 3x3 's all the way up to the 8x8. So they thought there were only 64 squares. Once they learned that there were a lot more squares, they guessed from 78 up to 250! Actually, we found that there are 204 squares. We also found a rule. If you have any size square, you square the number of units on one side of the square. Then you find the sum of all lesser numbers than the units on one side of the square squared.  For example, in the checkerboard, you would add 64 + 49 + 36 + 25 + 16 + 9 + 4 + 1   and get the total number of squares.

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