Seattle Infinity Math Circle

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Seattle Infinity Math Circle presents Who Wants
to Be a Mathematician?
Questions written by Joy Zheng
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Preliminary Round 1 (Green Eggs and Ham)
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Question 1 (100 points) Seattle Infinity Math
Circle has decided to hold a contest based on who
has the most green eggs and ham. The number of
times the letter e appears in this question
(not including the answer choices) in n! Find n.
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Correct Answer 4
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Question 2 (200 points) The Grinch snuck into a
household and stole all the presents under the
tree. When he arranged them in groups of 8, he
had 1 left over. When he arranged them in groups
of 14, he had 1 too few. What is the smallest
number of presents that he could have stolen?
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Correct Answer 41
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Question 3 (300 points) A piece of ham is placed
on top of an egg such that the area of the ham
not on top of the egg is equal to the area of the
ham on top of the egg. If the egg has radius 13
and the ham has side length 10, find the surface
area that the two take up when placed in this
manner, in terms of pi. Assume that eggs are
circular and pieces of ham are round.
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Correct Answer 169pi50
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Question 4 (400 points) The mysterious shadow is
making a potion to turn his eggs green. He must
use seventeen pints of water for every cup of
dye. If it takes 3 pints of potion to dye one
egg, how many pints of dye does he need to dye
105 eggs?
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Correct Answer 9
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Question 5 (500 points) It is rumored that the
recipe for green eggs and ham is buried at the
point that is equidistant from the points (7,
11), (2, 12), and (19, 29). Find this point in
(x,y,) coordinate form.
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Correct Answer (7, 24)
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Preliminary Round 2 (International Mosaics)
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Question 1 (100 points) Barbara wants to tile
her floor using regular polygons. Assuming that
she uses only one type of polygon, how many
different types of polygons (with different
numbers of sides) could she use?
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Correct Answer 3
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Question 2 (200 points) Barbara must tile a
straight road that leads from Seattle to Moscow.
She knows that the distance from Seattle to her
hometown is 343 miles, and that the distance from
Moscow to her hometown is 4956 miles. Find the
shortest possible distance between Seattle and
Moscow, in miles.
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Correct Answer 4613 (miles)
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Question 3 (300 points) A series of 25 students
walk down a hallway with 25 lockers. Student 1,
starting with locker 1, opens every locker.
Student 2, starting again with locker 2, reverses
the position (open/closed) of every 2nd locker,
and so on, for all 25 students. How many lockers
are closed at the end of this exercise?
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Correct Answer 20 (lockers)
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Question 4 (400 points) The value of one
triangular tile is equal to the value of 3 square
tiles. The value of 2 square tiles is equal to
the value of 7 hexagonal tiles. If the side
length of each tile is 1 unit and Kiara must
completely tile a 7 by 7 unit patch of floor
(going over the edges in allowed), which type of
tile would be the cheapest to use? Assume all
tiles are regular polygons.
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Correct Answer hexagonal
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Question 5 (500 points) Barbara and Kiara are
working together to tile a mosaic of the United
States. Barbara can tile 3 states per hour, and
Kiara can tile 14 states per hour. After they
tile for some amount of time, Malia, who can tile
7 states per hour, joins them. As soon as Malia
joins them, Kiara leaves. Barbara and Malia tile
together until until the job is finished. If
Barbara tiled exactly twice as many states as
Malia, how many states did Kiara tile, to the
nearest state?
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Correct Answer 35 (tiles)
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Preliminary Round 3 (Moo, Boo, and Too)
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Question 1 (100 points) Yay! Moo has traveled to
the fourth dimension! Find the distance between
the points (4, 5, 12, 14) and (7, 18, 0, 10).
Express your answer in simplest form.
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Correct Answer 13 sqrt 2
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Question 2 (200 points) Moo, Boo, and Too are
having a duel and cutting off each others
fingers. Moo cuts off two of Boos fingers. Boo
cuts of three of Toos fingers. Too cuts off one
of this own fingers. Boo cuts off one of Moos
fingers. Moo cutts of two of Toos fingers. Boo
cuts off half of Toos remaining fingers. Too
cuts off as many fingers from Boo as Boo has
already cut off, total, from Too. Moo cuts off
one more of Boos fingers. How many fingers does
Boo now have?
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Correct Answer 2 (fingers)
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Question 3 (300 points) Moo, Boo, and Too have
cats that are called Mow, Bow, and Tow (not
necessarily in that order). Moo has the oldest
cat. Bow is younger than Mow. Boos cat is not
Bow. If Toos cat is Bow, then Boos cat is not
Tow. Who has which cat?
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Correct Answer Moos cat is Tow, Boos cat is
Mow, and Toos cat is Bow.
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Question 4 (400 points) In an odd twist of fate,
Moo, Boo, and Too are somehow combined together
to form a single being with three brains, each of
which is active for some part of a day (there is
always at least one brain active at a given
time). Moos brain is active for exactly 22 hours
each day. Boos brain is active for exactly 11
hours each day. Toos brain is active for exactly
13 hours each day. The brains of Moo and Too are
active together for exactly 11 hours of each day.
The brains of Too and Boo are active together for
exactly 9 hours of each day. The brains of Boo
and Moo are active together for exactly 9 hours
each day. For how many hours each day are all
three brains active?
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Correct Answer 7 (hours)
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Question 5 (500 points) Mow, Bow, and Tow all
have leashes with length 50m. Mow has been tied
to a corner of a barn with dimensions 20m by 30m.
Bow has been tied to the corner of a barn with
dimensions 10m by 80m. Tow has been tied to the
corner of a barn with dimensions 40m by 40m. What
is the sum of the areas that the three cats can
roam over (does not include the barn)?
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Correct Answer 6400pi (square meters)
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Face-Off Question (The Crown Jewel)
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Face-off Question Someone just stole the crown
jewel of England! (gasp). The judge at the
trial was told all of the following as well as
the innocence or guilt of one of the suspects.
Here are their statements Suspect 1). I am
innocent. Suspect 2). Not including myself (no
matter if I am guilty or innocent), there are at
least 2 guilty people from these 4. Suspect 3).
Suspect 1 is guilty. Suspect 4). I am rather
confused. Also, it was somehow known that
everybody who was guilty lied, and that at least
one of the four was guilty. Given that the judge
(who is perfectly logical) was able to narrow the
field down to two possible suspects, which
suspects are they?
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Correct Answer Suspects 1 and 2