6.042/18.062J
Mathematics
for
Computer
Science
November
3,
2010
Tom
Leighton
and
Marten
van
Dijk
Problems
for
Recitation
15
1
The
Tao
of
BOOKKEEPER
In
this
problem,
we
seek
enlightenment
through
contemplation
of
the
word
BOOKKEEPER
.
1.
In
how
many
ways
can
you
arrange
the
letters
in
the
word
POKE
?
2.
In
how
many
ways
can
you
arrange
the
letters
in
the
word
BO
1
O
2
K
?
Observe
that
we
have
subscripted
the
O’s
to
make
them
distinct
symbols.
3.
Suppose
we
map
arrangements
of
the
letters
in
BO
1
O
2
K
to
arrangements
of
the
letters
in
BOOK
by
erasing
the
subscripts.
Indicate
with
arrows
how
the
arrangements
on
the
left
are
mapped
to
the
arrangements
on
the
right.
O
2
BO
1
K
KO
2
BO
1
BOOK
O
1
BO
2
K
OBOK
KO
1
BO
2
KOBO
BO
1
O
2
K
. . .
BO
2
O
1
K
. . .
4.
What
kind
of
mapping
is
this,
young
grasshopper?
5.
In
light
of
the
Division
Rule,
how
many
arrangements
are
there
of
BOOK
?
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2
Recitation
15
6.
Very
good,
young
master!
How
many
arrangements
are
there
of
the
letters
in
KE
1
E
2
PE
3
R
?
7.
Suppose
we
map
each
arrangement
of
KE
1
E
2
PE
3
R
to
an
arrangement
of
KEEPER
by
erasing
subscripts.
List
all
the
different
arrangements
of
KE
1
E
2
PE
3
R
that
are
mapped
to
REPEEK
in
this
way.
8.
What
kind
of
mapping
is
this?
9.
So
how
many
arrangements
are
there
of
the
letters
in
KEEPER
?
10.
Now
you
are
ready
to
face
the
BOOKKEEPER!
How
many
arrangements
of
BO
1
O
2
K
1
K
2
E
1
E
2
PE
3
R
are
there?
11.
How
many
arrangements
of
BOOK
1
K
2
E
1
E
2
PE
3
R
are
there?
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 Fall '10
 TomLeighton,Dr.MartenvanDijk
 Computer Science, Vowel, Diphthong, Consonant, E2 P E3, K2 E1 E2

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