Draft

# Monotonic sentences: A puzzle

Draft of 2013.03.06 ☛ 2015.04.04 ☛ 2016.07.16

Call a sentence “weakly monotonic” if when you stack the words on top of one another (like this)

c a l l _ _ _ _ _
a _ _ _ _ _ _ _ _
s e n t e n c e _
m o n o t o n i c
i f _ _ _ _ _ _ _


and read down the columns of letters, all the columns are alphabetical in top-to-bottom order—skipping blanks whenever a letter’s missing from a given column.

In the example, the first letters of the words are CASMI, so that sentence is not even weakly monotonic. Maybe that was a bad place to start.

The sentence “Boy dozes” is weakly monotonic:

b o y _ _
d o z e s


the “columns” are BD, OO, YZ, _E and _S, respectively, and (ignoring blanks) those are all in alphabetical order. “Ignoring blanks” is probably important. Let’s make it a rule that a blank space is a wildcard, and that we are only interested in letters as such. So spaces can appear in any place at all.

What’s the longest weakly monotonic English sentence?

Call a sentence “strongly monotonic” if you’re not allowed to skip missing letters, after any letter appears. That is, once a letter appears in a given position, there must be at least that many letters in all subsequent words.

So “Boy dozes” is both weakly and strongly monotonic.

What’s the longest strongly monotonic English sentence?