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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).
Noah the Patriarch
Built a big boat out of
Finding some grace in the
Eyes of Jehovah, this
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.
- There are two sets of four lines. These sets of four lines are called “quatrains.”
- 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)
- The only rhymes we need are at the end of the two quatrains.
- 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.
- 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.
- 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!