Fifth grader Aaradhya asks: "How do we find the factors of 342, 450 and 540 without a calculator?"

That's a really good question! The best suggestion I can give you is to make sure you are familiar with some divisibility rules. These are very helpful tools in breaking a number down into their factors.

For example, we know that any number that ends with an even digit is a multple of 2. So, right off the bat, we can divide 342 by 2. Of course, without a calculator you'll need to do long division. But then you've got smaller numbers to work with. In this case, 342 divided by 2 is 171.

Does that have any factors? Well, here's where the divisibility rule for 3 might come into play. A number is divisible by 3 if the sum of its digits is divisible by 3. Since 1 + 7  + 1 = 9, and 9 is divisible by 3, then we know 171 is divisible by 3 also. So, another quick long division and we've got 57. Once again, 5 + 7 is divisible by 3, so we know 57 is also. We continue like this until we get down to a number that is prime - in this case, 19. Thus, the factors of 342 are 1, 2, 3, 19, and 342.

There are other useful divisibility rules - for example, if a number ends with a zero, that means it's divisible by 10. Thus, 450 is 10 times 45. Then we just break these down iunto smaller and smaller factors.

Similar to this rule, if a number einds in zero or five, it's divisible by 5.

There are other divisibility rules, but they get increasingly complicated. The rules for seven and thirteen are so cumbersome that I never use them. The divisibility rule for 11 requires you to alternately add and subtract the digits to see if the sum is a multiple of eleven.

For example, 14641 is a multiple of 11 because 1 - 4 + 6 - 4 + 1 = 0 , which is divisible by 11.

Without the divisibility rules, this process requires a lot of long division just to find out if a number is a factor. You still may need to do some of that, but the divisibility rules will help you keep that to a minimum!

The Professor Puzzler blog has been pretty quiet recently, so I'm breaking the monotony by asking myself a question.

Me: Professor Puzzler, what is a Double-Dactyl poem, and how do you write one?

Other Me: That's a great question! I hesitate to say that the Double-Dactyl is one of the silliest poetry forms in existence, but…well…it’s one of the silliest poetry forms in existence.

Let’s start with a Double-Dactyl example, and then we can dissect it to understand how the form works. This is a poem about Noah (yes, the guy with the ark).

Splishity splashity
Noah the Patriarch
Built a big boat out of
Gopher-wood trees

Finding some grace in the
Eyes of Jehovah, this
Antediluvian
Sailed o'er the seas

Before we get into the rules, what is a dactyl? A dactyl is a metrical foot which consists of one stressed syllable followed by two unstressed syllables. In other words, it sounds a bit like a waltz. OOOM-pah-pah OOOM-pah-pah. Okay, now let’s dive in.

1. There are two sets of four lines. These sets of four lines are called “quatrains.”
2. In each quatrain, the first three lines are each two dactyls. The last line of each quatrain is a single dactyl followed by one accented syllable (OOOM-pah-pah-OOOM)
3. The only rhymes we need are at the end of the two quatrains.
4. The first line must be nonsense words. Since they’re nonsense, they don’t have to have anything to do with the subject of the poem, but it can be fun – as I did in my Noah poem – to make them similar to real words that connect to the subject of the poem.
5. The second line must be a proper noun. This would most commonly be a person’s name (or name and title), but could also be a place, organization name, or even something like “U.S.S. Nautilus.” In the example above, NO-ah the PA-tri-arch has the accents on NO and PA, with the other syllables unaccented.
6. Somewhere in the poem – preferably in the second quatrain, and usually the sixth line of the poem (but the location is not a hard-and-fast rule), there must be a line that consists of a single six-syllable word that fits the dactyl rhythm. In the Noah poem, that word is “antediluvian” (which means “before the flood”).

There you have it – now you’re ready to write your own Double-Dactyl. On my YouTube channel (link: Doug's ventiloquism, music, and teaching) my puppets (yes, I’m a ventriloquist!) and I will posted a series of three Double-Dactyls. The third in the series is actually sung instead of recited; if you learn the tune, that may help you write your own Double-Dactyls!

Wiffity Woffity (a poem about a timberwolf and a dodo bird)

Axity Waxity (a poem about George Washington and a cherry tree)

Offity Scoffity (a poem about Alice in Wonderland)

Note that in my poems, my nonsense words all end in “-ity” but that is not a requirement; I just like the way it sounds. I guess I just got stuck in a nonsense rut.

Finally, if you’re interested in other kinds of poetry, one of my puppets shares his own rendition of Robert Burns’ “My Love Is Like a Red, Red Rose,” and several of my puppets have done limericks: Jeorge’s Limerick, Jeffrey’s Limerick, Professor Jameson’s Limerick, Doctor Jonas’ Limerick.

And for those who like Star Wars, be on the lookout for some Star Wars themed Double Dactyls late in 203!