MATH 239 Spring 2010 Assignment 3
Due: May 28, 2010, 11:45AM EDT
1. In the Kingdom of Shallitland, King Jeffrey XVI declared that citizens of his coun
try (the Shallites) must use coins of these denominations: 1 byte, 7 bytes, 57 bytes,
80 bytes. Let
n
be a positive integer.
(a)
(2 marks)
Assuming an endless supply of coins available in each denomina
tion, determine the number of ways that a collection of Shallite coins can
make up
n
bytes. Write this as the coefﬁcient in a rational function.
(b)
(2 marks)
King Jeffrey XVI ordered the 7byte coins to be made of expensive
silicon, and made a restriction that each citizen may possess at most 8 of these
7byte coins. Given this restriction, determine the number of ways that one
Shallite citizen can use their own coins to make up
n
bytes. Write this as the
coefﬁcient in a rational function.
(c)
(2 marks)
Let
a
n
and
b
n
be the answers for parts (a) and (b) respectively. Using
your answers in (a) and (b), show that
a
n
≥
b
n
for all
n
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '09
 M.PEI
 Math, Rational function, Recurrence relation, King Jeﬀrey XVI

Click to edit the document details