# What is a Scalable Phrase™?

Now that you are familiar with Cyclone Phrases, let's look at another kind of phrase.

If a phrase adheres to a certain rule, then I call it a Scalable Phrase™.

Use the examples below to find the rule.

EDIT: I added the visual tag as a hint.

If you liked this puzzle, try others like it:
What is a Cyclone Phrase™?

If you are coming from the left to the right, then "Scalable Phrases" are climbable while "Non-Scalables" are not climbable. Scaling a phrase refers to climbing it.

For a phrase to be climbable it has to be composed of climbable letters.

A climbable letter is any letter that, if you are on the "floor" (where the letter sits) then you can "climb" up the letter because no angle from the bottom to the top is greater than 90 degrees, or perpendicular from the floor. For example, V is not climbable because coming from the left the first obstacle (the \ of the V) is sort of an overhang. T is also not climbable even though the beginning is climbable, but then at the overhang it is not. H, F, E, M, etc are all climbable letter because they have no overhang.

Notice that I in the font chosen IS climbable, although in many fonts it is not, since it has an overhang.

Here is a full list of climbable letters:
ABDEFHIKLMNPR

Here is a full list of nonclimbable letters:
CGJOQSTUVWXYZ

Really nice puzzle!!

• Yes, this is it! Excellent that you also went into great detail about overhangs and angles, and also pointed out the dependency on fonts!
– JLee
Jun 17, 2015 at 12:59
• @JLee: Can't wait for what kind of words you're gonna come up with next! Jun 17, 2015 at 13:11

I notice that:

all the letters in scalable phrases touch the bottom left corner of their bounding box — that if you were to place them in the first quadrant of the Cartesian plane with the bottom left corner touching the origin, you could "scale" them up without changing their anchor.

All the non-scalable phrases

contain at least one letter that doesn't follow that rule.

• Yep, just noticed this too. It would explain why A and F are in the scalable words but T and W are not. Jun 17, 2015 at 1:58
• +1 Nice answer, Joe. That wasn't my idea on how the word scalable fit into things, but it's a valid statement nonetheless.
– JLee
Jun 17, 2015 at 2:45
• I guess the bounding box for the letter I is just the letter then, with no white space?
– JLee
Jun 17, 2015 at 2:48
• Yeah, it would be.
– user88
Jun 17, 2015 at 3:28
• @JLee: Is it close enough to your intended answer that you can reveal it now?
– user88
Jun 17, 2015 at 3:28

It must be relevant that when

we replace each letter by its corresponding number in the alphabet (A=1, B=2, etc.),

we find that in each of "MALE AND FEMALE" and "DREADED DREAM",

the phrase splits into two halves each of which has letters summing to the same total.

Explicitly, in "MALE AND FEMALE" we have

13+1+12+5+1+14 = 46 = 4+6+5+13+1+12+5

4+18+5+1+4+5+4 = 41 = 4+18+5+1+13.

The exact same statement doesn't hold for all the example phrases given, but perhaps something along the same lines does. I tried the possibility of

replacing "two halves" by "$n$ $n$ths for some $n$" (i.e. we might be able to split some of the phrases into three thirds or four quarters all with equal letter-sums).

That didn't work, but maybe something else...

• I added a tag hint.
– JLee
Jun 17, 2015 at 0:07

All of the letters in a scalable phrase

have a straight stem: ABDEFHIKLMNPR (used in the clues). Some additional straight-stemmed letters appear in the counter-examples, but except for W they are all used in conjunction with a round letter: TVWZ. The stemmed letter X is not used in the clues or counterexamples.

• This rule fails for WALKED A MILE, so it’s not exactly right. Trying to figure out how to cover that case too. Jun 17, 2015 at 1:05
• Walked a mile is not a scalable phrase - Ran is.
– user88
Jun 17, 2015 at 1:53
• @JoeZ. Right, which is why this rule is not exactly right. I think I may be on the right track, but have not quite identified the right trait. Jun 17, 2015 at 1:54
• @JLee Thanks! I was so close to getting this one! The main thing that threw me was letters like F, which are scalable from the left but not the right. Jun 17, 2015 at 20:15
• @BraddSzonye Yeah you were on the right track. I thought about including some sort of left-to-right hint into the puzzle, but I finally decided against it, convincing myself that the left-to-right order of reading would be the unspoken "hint" for left-to-right.
– JLee
Jun 17, 2015 at 20:19