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Hello citizens. Many of you may have heard of a North American competition
called "The University of Waterloo Pascal Contest." I was a candidate in this
competition, as well as many other grade 9 students across North America.
The test booklet is arranged into three parts with a total of 25 questions. The final
five
questions are supposed to be the hardest and most challenging. You are given
one hour to complete all 25 questions, and all questions are multiple choice
possibilities. If you answer a question wrong, you receive no marks, if you
answer one of the final 5 questions correctly, you receive 8 marks each. If you
leave a question unanswered, you receive 2 free credits.
Here are questions #21-24, which I will use to test the citizens of Whyville.
Whoever can achieve the highest results on the following four questions will
receive 500 clams from me!
1. In the diagram, the number of different paths (from top to bottom) that spell
"PASCAL" is
a) 6 b) 10 c) 12 d) 16 e) 24
P
A A
S S S
C C
A
L L
2. A container in the shape of a cube has edge length 20cm and contains some
water. A solid gold cube, with edge length 15cm, sinks to the bottom of this
container, causing the water level to rise just to the top of the solid cube.
Which of the following is closest to the original depth of the water?
a) 6.56cm b) 8.25cm c) 10.50cm d) 5.31cm e) 7.50cm
3. A driver approaching a toll booth has exactly two quarters, two dimes, and
two nickels in his pocket. He reaches into his pocket and randomly selects two
of these coins. What is the probability that the coins that he selects will be
at least enough to pay the 30-cent toll?
a) 3:5 b) 2:5 c) 1:3 d) 3:10 e) 2:3
4. In the sequence of fractions 1/1, 2/1, 1/2, 3/1, 2/2, 1/3, 4/1, 3/2, 2/3,
1/4, 5/1,..., fractions equivalent to any given fraction occur many times. For
example, fractions equivalent to 1/2 occur for the first two times in positions
3 and 14. In which position is the fifth occurrence of a fraction equivalent to
3/7?
a) 1207 b) 1208 c) 1209 d) 1210 e) 1211
I hope you have a fun time trying to answer all of these questions. You are
supposed to only have 25 minutes for these four questions, but I will allow one
week from the date this article is published for the best answers that you can
come up with.
To send your answers, y-mail Deriko with subject title: "Trivia." Write the
letter corresponding to the answer of your questions at the top of the y-mail,
and any additional information you wish to tell me below your answers.
Thanks for taking part.
Deriko
The original test is here:
http://contest-cemc.uwaterloo.ca/past_contests/2004/2004_pascal_contest_e.pdf
The makers of the Pascal test are here: http://cemc.uwaterloo.ca/
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