This preview shows pages 1–2. Sign up to view the full content.
The University of Sydney
MATH 1004
Second Semester
Discrete Mathematics
2011
Tutorial 1 Week 2
1.
Which of the following strings of brackets are balanced? In each case, explain
carefully why the string is, or is not, balanced:
(
i
)
((()()
(
ii
)
(())()
(
iii
)
())(()
2.
Suppose you have numbers
x
0
,
x
1
,
x
2
,
. . .
,
x
n
and you want to multiply
them together. In how many ways can you insert brackets into the string
x
0
x
1
x
2
. . . x
n
so that the order of multiplication is completely speciFed? Each
pair of brackets should contain just two terms. ±or example, when
n
= 2, there
are two ways: (
x
0
(
x
1
x
2
)) and ((
x
0
x
1
)
x
2
). Try
n
= 3 and
n
= 4.
3.
Consider a river system with
n
sources which eventually merge to form a single
stream. Assuming that no more than two streams merge at any point, we are
interested in the number of ways that the mergers can take place.
(
i
)
Compile a table of values for
n
= 1, 2, 3, and 4 and then Fnd (guess) a
general formula.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
 Three '11
 various

Click to edit the document details