Problem-Solving:

Mathematical Palindromes

 

Today's Snack: Line up your palindrome snack on a small plate: an apple slice, followed by an orange slice, followed by another apple slice, followed by an orange slice, and finally - you guessed it! - another apple slice. Drink a glass of milk to go with it, only drink it walking backwards to make it a true palindrome beverage.

 

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Supplies:

Scratch paper and pencil

 

                       

There's an old joke going around (a really, really old joke) that claims that the very first thing Adam said to Eve was a palindrome. A palindrome (pronounced "PAL in droam") is a group of letters that read the same way forward as they do backward. It can be a word, a phrase or a sentence. Here's what Adam supposedly said - and have fun reading it backwards as well:

 

Madam, I'm Adam.

 

Another palindrome is:

 

Poor Dan is in a droop.

 

Then there's:

 

Mr. Owl ate my metal worm.

 

Never odd or even

 

Radar

 

Bob

 

. . . and many more. But did you know that palindromes can be NUMBERS, too?

 

By using addition, you can turn almost any number into its palindrome in just a few steps. For some reason, the only number ever found that doesn't work for this is the number 196, so don't choose it!

 

This will give you outstanding practice in addition, unless you pick one of the numbers that turn into a palindrome after just one addition or two.

 

You'll probably want to start with a two-digit number that is not already a palindrome. So, for example, you couldn't choose "44," but how about "49"?

 

Reverse the number and add it to the first number:

 

        49

    + 94

                 143

 

            Now reverse that number and add those two together:

 

                 143

              + 341

                 484

 

AHA! You have a palindrome after just two additions.

 

Now let's try the number 86:

                    86

                + 68

                 154

              + 451

                 605

              + 506

              1,111

 

            So 86 becomes a palindrome after three additions.

 

Are you ready to try? Pick a different two-digit number and start the additions on your scratch paper. Beware of 89 or 98, though - they become palindromes after TWENTY-FOUR additions!

 

            If you're up for bigger numbers, you can try a three-digit number next, and then a four-digit number, but caution: 739 takes SEVENTEEN additions. So you'll be adding until you . . . here comes another palindrome . . . POP!