Homework 3
Math 299, Fall 2009
Old Problems:
1. The integer 52009 has 1,405 digits, and its rst digit is a 1. For how many integers
1 k 2009 does 5k begin with the digit 1?
2. Find a positive integer n, not a power of 10, such that the initial digits of n
Seminar 1 Problems
Math 299, Fall 2009
Here are the problems that we covered in class on the rst day (September 1).
Problem 1. What is the units digit of 132009 ?
Solution:
It is possible to determine the units digit of a product from the units digit of
e
Homework %
Math 299, Fall 2009
Old Problems:
1. The integer &#!* has ",%!& digits, and its first digit is a ".
" 5 #!* does &5 begin with the digit "?
For how many integers
2. Find the area of the region in the plane defined by the inequality
kB '!k kCk k
Homework 5
Math 299, Fall 2009
Old Problems:
1. The integer &#!* has ",%!& digits, and its first digit is a ". For how many integers
" 5 #!* does &5 begin with the digit "? (Note: The answer to this problem is '!&, but
there has not yet been a complete so
Homework 2
Math 299, Fall 2009
Problems from Last Week:
1. The increasing sequence 1, 3, 4, 9, 10, 12, 13, . . . consists of all those positive integers
which are either powers of 3 or sums of distinct powers of 3. Find the 100th term of
this sequence.
2.
Homework 1
Math 299, Fall 2009
1. The sum of two 4-digit palindromes is a 5-digit palindrome N . Compute the maximum
possible value for N .
2. Find the smallest positive integer multiple of 15 whose digits are all either 8 or 0.
3. The sum of four two-dig