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# Math patterns: table

Video transcript

So let's say I have tables where
I can fit one person at either of the short ends of the table. So I could fit one person there. I could fit one person there. You could view this as we're
looking from above the table here. So we could put one
person at either of the short ends of the table. And then on these longer
ends right over here, we can fit two people. We can fit two people
at the longer end. So when you have one table,
you could fit one, two, three, four, five, six people. You could fit six people. Now let's think
about what happens as we add tables end to end
to this table right over here. So let's imagine now two tables. So here we have
one table, and it's going to touch ends with
this table right over here. And because it touches
ends right over here-- we're making it one
big continuous table-- you can't fit
someone here anymore. So now how many
people can we fit? Let's see. We can fit one, two,
three, four, five. And then on this table,
which is identical, you could fit six,
seven, eight, nine. And then you could
put one person at the end right over here. So when you have two
tables end to end, you can fit a
total of 10 people. Let's keep going and see if we
can think of a pattern here. So let's put three
tables here-- so one table, two tables,
and three tables. So just as before, we
could put one at each end. So that's two people. Then we have 3, 4, 5, 6,
7, 8, 9, 10, 11, 12, 13, 14 folks-- 14 folks. So what does it look
like is happening here. Well if you just
look at the numbers, we went from 6 to 10 to 14. It looks like we're adding four
people every time we actually add a table. Now does that
actually makes sense? So let's think about
this first situation. Let's imagine these
are real people, and I'll make this person
in blue right over here. If you were to bring
over this new table, if you bring over table
two-- so this is table one-- this blue person has to move. And so where could they move? Let's say that
they always insist on sitting at the
end of a table. So the blue person moves to
the new end of the table. They move right over here. So how many new people could
move to this combined table now that you brought
this second table in? Well the new people I will
do in this purple color. The new people are
that person-- let me do it in a more unique
color-- this person, this person, this
person, and this person. So you were able to add four
new people with the new table. One way to think about
it is a new table is going to have
one usable end here. That usable end is going to
be taken by the person who was already at the usable end
of when you had less tables. And so the real addition
is the two sides here. So you're adding four people
every time you add a table. So it makes complete sense. So based on this, you
could think about, without even having to draw
these diagrams, how many people you would be able to fit
if you had four or five or six or however many tables. So you could imagine,
if you have four tables, we just have to
add four, and you should be able to sit 18 people. If you have five
tables, you should be able to fit 22 people
and on and on and on.