# What is a Self-cancelling Word™?

This is in the spirit of the What is a Word/Phrase™ series inaugurated by JLee with his original Phrase™ and Word™ puzzles.

If a phrase adheres to a certain rule, then I call it a Self-cancelling Word™.

Use the examples below to find the rule.

In case you want it in CSV:

Self-cancelling Words™, Not Self-cancelling Words™
WARM, HOT
CUSTOMIZE, PERSONALIZE
STOPPED, BLOCKED
PICTURE, IMAGE
FRIGHTENING, SCARY
ARRANGEMENT, LAYOUT
HIGHWAY, FREEWAY
PHOTOGRAPHER, PAPARAZZI
NUMEROUS, MANY
FAILING, DECLINING
BOXING, BATTLING
OVER, ACCOMPLISHED


The puzzle relies on the series' inbuilt assumption, that each word can be tested for whether it is a Self-cancelling Word™ or not on its own.

Hint :

Self-cancelling Words™ are found using a cursive font.

• No incoming hints? – Techidiot Nov 9 '16 at 8:32
• @Techidiot Is that a request :-)? – IAmInPLS Nov 9 '16 at 9:04
• Haha. Yess. Offcourse if you don't mind. – Techidiot Nov 9 '16 at 9:06

A self-cancelling word...

When written in lower-case has the same number of tall letters (letters like $bdth$ that are taller than the letter $a$ for example) as letters that dip below the writing line (letters like $pq$).

It could be said that these two types 'cancel' each other out.

N.B.

This only works with a cursive font, where the $\mathfrak{z}$ dips below the writing line and the $f$ is both tall and dips below the writing line (effectively 'cancelling' itself out).

Also, $i$ is not counted tall despite the dot!

For example...

$\mathcal{warm}$ is self-cancelling as it has no tall or dipping letters.

$\mathcal{photographer}$ is self-cancelling as it has three tall letters ($hth$) that cancel three dipping letters ($pgp$).

$\mathcal{personali}\mathfrak{z}\mathcal{e}$ is not self-cancelling as it has an uneven two dipping letters ($p\mathfrak{z}$) to one tall letter ($l$).

$\mathcal{accomplished}$ is not self-cancelling as it has only one dipping letter ($p$) to three tall letters ($lhd$).

Update

The correct term for portions of letters that are tall or dipping are ascenders and descenders (thanks to @IAmInPLS for the links).

• About the 'i' : en.wikipedia.org/wiki/Ascender_(typography) – IAmInPLS Nov 9 '16 at 10:42
• @IAmInPLS thanks for the edit! Great Puzzle! – Arth Nov 9 '16 at 16:44
• @GPR did the cursive font, it looks really good :-). Thank you for solving it, good job! – IAmInPLS Nov 9 '16 at 16:47