Tutoring need for intro college math course
Budget: $10 – $30 CAD
Samples of questions that require assistance...
Suppose that, instead of being connected in a line, there are 6 caves connected in a circle (so
that there is a tunnel from the last room back to the first room). Come up with a strategy that
guarantees Elmer will catch Bugs, or explain why no such strategy exists.
Consider again the circular case as in the previous question. Elmer Fudd has now enlisted the
help of Yosemite Sam to catch Bugs. If there are 6 caves, come up with a strategy that will
guarantee they will catch Bugs (Sam and Elmer each look in one cave on each day). You get
more marks for coming up with a more efficient solution
Each published book is identified by a number known as its ISBN. This is a ten-digit number found
on the back of the book. The first nine digits contain information about the language, publisher, etc.
The tenth digit is a check digit. If the first nine digits are abcdef ghi, the tenth digit, j, is chosen so
that
10a + 9b + 8c + 7d + 6e + 5f + 4g + 3h + 2i + j ≡ 0 (mod 11).
If j is 10, an X is used instead.
(a) Suppose the first nine digits of an ISBN are 0-393-32663, what is the tenth digit?
(b) Will the ISBN detect an error where two adjacent integers are interchanged (like in the telephone
number puzzle)? Explain.
(c) Suppose that abcdehghij is a valid ISBN, and suppose that d ̸ = d′. Show that abcd′ef ghij is
no longer a valid ISBN. Explain why a similar argument would work for any other single digit
as well (for example g ̸ = g′), you do not need to repeat the argument, just explain why it works
for all digits. (Note: Here you have shown that the ISBN system detects any single digit error)
Suppose that, instead of being connected in a line, there are 6 caves connected in a circle (so
that there is a tunnel from the last room back to the first room). Come up with a strategy that
guarantees Elmer will catch Bugs, or explain why no such strategy exists.
Consider again the circular case as in the previous question. Elmer Fudd has now enlisted the
help of Yosemite Sam to catch Bugs. If there are 6 caves, come up with a strategy that will
guarantee they will catch Bugs (Sam and Elmer each look in one cave on each day). You get
more marks for coming up with a more efficient solution
Each published book is identified by a number known as its ISBN. This is a ten-digit number found
on the back of the book. The first nine digits contain information about the language, publisher, etc.
The tenth digit is a check digit. If the first nine digits are abcdef ghi, the tenth digit, j, is chosen so
that
10a + 9b + 8c + 7d + 6e + 5f + 4g + 3h + 2i + j ≡ 0 (mod 11).
If j is 10, an X is used instead.
(a) Suppose the first nine digits of an ISBN are 0-393-32663, what is the tenth digit?
(b) Will the ISBN detect an error where two adjacent integers are interchanged (like in the telephone
number puzzle)? Explain.
(c) Suppose that abcdehghij is a valid ISBN, and suppose that d ̸ = d′. Show that abcd′ef ghij is
no longer a valid ISBN. Explain why a similar argument would work for any other single digit
as well (for example g ̸ = g′), you do not need to repeat the argument, just explain why it works
for all digits. (Note: Here you have shown that the ISBN system detects any single digit error)