THE UNIVERSITY OF BRITISH COLUMBIA
Homework 1
Math 414 Section 101
Due by 1pm on Sept. 13, 2013
1. Mark has a bag that contains 3 black marbles, 6 gold marbles, 2 purple marbles,
and 6 red marbles. Mark adds a number of white marbles to the bag and tells
Susan that if she now draws a marble at random from the bag, the probability of it
being black or gold is 3/7. How many white marbles does Mark add to the bag?
2. A six-digit number has the property that if its first three digits, as a block, are
interchanged with its last three digits then the number is six times as large. There
is only one such number. Find this number, and explain why it is the only one.
3. Alex has red tokens and blue tokens. There is a booth where Alex can give
two red tokens and receive in return a silver token and a blue token, and another
booth where Alex can give three blue tokens and receive in return a silver token
and a red token. Alex continues to exchange tokens until no more exchanges are
possible. How many silver tokens will Alex have at the end?
4. P, Q, R, S, and T are five different integers between 2 and 19 inclusive.
• P is a two-digit prime number whose digits add up to a prime number.
• Q is a multiple of 5.
• R is an odd number, but not a prime number.
• S is the square of a prime number.
• T is a prime number that is also the mean (average) of P and Q.
Which number is the largest? Show your work.
5. Invent a grade 8-10 workshop problem and write out a detailed solution for
someone giving a workshop. Take as inspiration some UBC Grade 8-10 workshop
problem from 2009-2010. Identify explicitly the problem you used. Alternatively
you may use another source (and identify it) or create a problem using your own
imagination.
Note: Please make a photocopy or handwritten copy of the problem you create in
question 5 and hand it in as the same time as the homework.