If
you
haven’t
seen
before
why
eight
‘buffalo’
strung
together
form
a
valid
English
sentence,
then
strap
in
for
a
linguistic
trip.
Buffalo
has
at
least
three
meanings:
as
a
collective
noun
it
refers
to
bison,
as
a
proper
noun
it’s
a
city
in
New
York,
and
as
a
verb
it
means
to
bewilder.
The
eight-buffalo
sentence
uses
all
three
meanings,
so
let’s
decipher
it
by
substituting
each
with
a
similar
word.
We’ll
use
‘bulls’
for
the
animals,
‘French’
for
hailing
from
France,
and
‘bewilder’
for
the
verb.
With
this
translation,
Buffalo buffalo Buffalo buffalo buffalo buffalo Buffalo buffalo
becomes
French bulls French bulls bewilder bewilder French bulls.
Okay, not much easier to understand. Largely because the sentence omits some implied words:
French bulls (who other) French bulls bewilder (then go on to) bewilder (yet another group of) French bulls.
The sentence says that bulls who get bewildered by other bulls then go on to bewilder yet more bulls, and also all the bulls are French. The eight-buffalo construction is really commentary on the never-ending cycle of animal bewilderment in upstate New York.
The neat sentence almost always appears in this eight-word form, but amazingly you can string together any number of buffalo to form a valid sentence! From the single “Buffalo!” exclamation of an animal sighting, to the double “Buffalo buffalo” observation that bulls tend to bewilder, all the way to a thousand buffalo in a row.
To see this, suppose you have a string of n buffalo and it forms a valid sentence. If any of your animals don’t already hail from New York, then you can extend the sentence by inserting a Buffalo (turn a bull into a French bull). But if all of your bulls are already French, then you can change one French bull to “bulls that other bulls bewilder.” Repeating these transformations generates longer and longer grammatically correct sentences.
The phenomenon works with any word that can triple as a collective noun, verb, and adjective. Another example is “police,” which refers to officers of the law, the act of enforcing that law, and a town in Poland.
Try to wrap your mind around more grammatical oddities below.
Did you miss last week’s puzzle? Check it out here, and find its solution at the bottom of today’s article. Be careful not to read too far ahead if you haven’t solved last week’s yet!
Puzzle #42: Grammatically Correct
Some
of
these
are
famous
questions,
so
if
you’ve
seen
them
before,
then
please
refrain
from
answering
in
the
comments
to
give
newcomers
a
shot.
Punctuate the following so that they make sense:
that that is is that that is not is not is that it it is James while John had had had had had had had had had had had a better effect on the teacherBelow, fill in the three blanks with the same letters in the same order so that the resulting sentence makes sense. You may add spaces between letters as needed:
The ____ doctor was ____ to operate on the patient because there was ____.
For example, “I ____ wish my doctor would tell me ____ when she was free for an appointment” could be completed with “sometimes” and “some times,” respectively.
I’ll
be
back
Monday
with
the
answers
and
a
new
puzzle.
Do
you
know
a
cool
puzzle
that
you
think
should
be
featured
here?
Message
me
on
X
@JackPMurtagh
or
email
me
at
Solution to Puzzle #41: Time Warp
If
you
managed
to
solve
last
week’s
difficult
clock
puzzle,
then
you
may
have
too
much
time
on
your
hands.
If
you
swap
the
hour
hand
and
the
minute
hand
on
an
analog
clock,
how
many
possible
valid
times
can
it
still
display?
Quick
aside, in
case
what
I
meant
by
“valid
time”
was
not
clear
in
the
problem
statement:
not
all
possible
positions
of
the
hands
actually
occur
on
a
normal
functioning
clock.
For
example,
there
is
never
a
moment
during
the
day
when
both
hands
point
directly
at
the
3.
Because
at
3:00,
the
hour
hand
points
at
the
3,
but
the
minute
hand
points
at
the
12.
At
3:15,
the
minute
hand
points
at
the
3,
but
the
hour
hand
is
now
a
quarter
of
the
way
to
the
4.
Hand
positions
that
actually
occur
on
a
typical
functioning
clock
I’m
calling
“valid.”
The
answer
to
the
puzzle
is
143.
There
are
a
few
ways
to
tackle
this.
I
think
the
explanation
below
is
pretty
slick,
but
for
a
more
detailed
mathematical
approach,
check
out
Enfy’s
solution
in
last
week’s
comments.
We want to know for how many positions of the hands on a typical (unmodified) clock can we swap the two hands and still display a valid time. Note that on clocks, the minute hand moves 12 times faster than the hour hand (when the minute hand completes one revolution, the hour hand moves one twelfth of the way around the clock face). Our trick will be to imagine adding an extra hand that moves 12 times faster than the minute hand. This effectively models two different clocks at once: The hour hand and minute hand behave like a normal clock while the minute hand and extra hand behave like a sped up clock, but because their relative speed is preserved (one moves 12 times faster than the other) they still form all of the same positions as a normal clock with the minute hand taking the role of the hour hand.
So we have one clock where the minute hand behaves like a minute hand, and another one where the minute hand behaves like an hour hand. On this view, the interchangeable times occur whenever the hour hand and the extra hand overlap. The true hour and minute hands always form a valid time, and if we swap them when the hour and extra hand overlap, then the minute hand assumes the role of the extra hand (which was acting like a minute hand) while the hour hand assumes the role of the minute hand (which was acting like an hour hand).
The extra hand moves 144 times faster than the hour hand (12 x 12). They begin overlapping at noon, and then every time the extra hand does one revolution, it will overlap with the hour hand once. The last of these overlaps will occur at midnight, which in our stipulations we’re not counting as distinct from noon. So the number of valid times is 143.