Transcript The Lion - Shambles

The Lion
Team Competition
• Welcome to the team competition. This is the
event where using all your teammates to
optimize your time will be essential.
• Each question will have a different allotment of
time and each question varies in difficulty.
• For each question you may score 2 points. One
point for a speed answer and a second point for
your final answer. (Note: to get the speed
answer point it must be same correct answer as
your final answer.)
• Let’s do a practice question!
Practice question time:
Speed answer: 2 minutes
Final Answer: 3 minutes
Practice question
In Circle Land, all rules of mathematics are the same as we
know them except numbers are shown in the following way:
Calculate the following expression and provide the answer
as they would in Circle Land?
Practice question
In Circle Land, all rules of mathematics are the same as we
know them except numbers are shown in the following way:
Calculate the following expression and provide the answer
as they would in Circle Land?
STOP
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Practice question answer
Now for the real thing. Good luck.
Question #1 time:
Speed answer: 3 minutes
Final Answer: 4 minutes
Question #1
In the diagram, ABCD
is a square with area
25 cm2 . If PQCD is a
rhombus with area 20
cm2.
What is the area of
the shaded region?
Question #1
In the diagram, ABCD
is a square with area
25 cm2 . If PQCD is a
rhombus with area 20
cm2.
What is the area of
the shaded region?
STOP
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Question #2 time:
Speed answer: 4.5 minutes
Final Answer: 6 minutes
Question #2
A hat contains n slips of paper. The slips of
paper are numbered with consecutive even
integers from 2 to 2n. Consider the situation
where there are six slips of paper (n = 6), in
the hat, two students, Tarang and Joon, will
each choose three slips from the hat and sum
their total. In this situation (when n=6) it is
impossible for them to have the same total.
If more slips of paper are added to the hat,
what is the smallest value of n > 6 so that
Tarang and Joon can each choose half of the
slips and obtain the same total?
Question #2
A hat contains n slips of paper. The slips of
paper are numbered with consecutive even
integers from 2 to 2n. Consider the situation
where there are six slips of paper (n = 6), in
the hat, two students, Tarang and Joon, will
each choose three slips from the hat and sum
their total. In this situation (when n=6) it is
impossible for them to have the same total.
If more slips of paper are added to the hat,
what is the smallest value of n > 6 so that
Tarang and Joon can each choose half of the
slips and obtain the same total?
STOP
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Question #3 time:
Speed answer: 2 minutes
Final Answer: 3 minutes
Question #3
The Fryer Foundation is giving out four
types of prizes, valued at $5, $25, $125 and
$625.
There are two ways in which the Foundation
could give away prizes totaling $880 while
making sure to give away at least one and at
most six of each prize. Determine the two
ways this can be done.
Question #3
The Fryer Foundation is giving out four
types of prizes, valued at $5, $25, $125 and
$625.
There are two ways in which the Foundation
could give away prizes totaling $880 while
making sure to give away at least one and at
most six of each prize. Determine the two
ways this can be done.
STOP
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Question #4 time:
Speed answer: 2 minutes
Final Answer: 3 minutes
Question #4
A Nakamoto triangle is a right-angled
triangle with integer side lengths which are
in the ratio 3 : 4 : 5. (For example, a triangle
with side lengths 9, 12 and 15 is a
Nakamoto triangle.) There are three
Nakamoto triangles that have a side length
of 60. Find the combined area of these
three triangles.
Question #4
A Nakamoto triangle is a right-angled
triangle with integer side lengths which are
in the ratio 3 : 4 : 5. (For example, a triangle
with side lengths 9, 12 and 15 is a
Nakamoto triangle.) There are three
Nakamoto triangles that have a side length
of 60. Find the combined area of these
three triangles.
STOP
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Question #5 time:
Speed answer: 3.5 minutes
Final Answer: 5 minutes
Question #5
• Let s be the number of positive integers from 1 to
100, inclusive, that do not contain the digit 7.
• Let t be the number of positive integers from 101
to 300, inclusive, that do not contain the digit 2.
• Let f be the number of positive integers from
3901 to 5000, inclusive, that do not contain the
digit 4.
Determine the value of s+t+f.
Question #5
• Let s be the number of positive integers from 1 to
100, inclusive, that do not contain the digit 7.
• Let t be the number of positive integers from 101
to 300, inclusive, that do not contain the digit 2.
• Let f be the number of positive integers from
3901 to 5000, inclusive, that do not contain the
digit 4.
Determine the value of s+t+f.
STOP
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Question #6 time:
Speed answer: 3 minutes
Final Answer: 4 minutes
Question #6
Amanda has the following
grades on her Calculus
tests this past year. She
can’t remember her grade
on her Parametrics test but
she does remember that her
worst test was Applications
of Integration. She took her
Polar test today but has no
idea how she did on it.
What is the difference
between her highest
possible average for the
year and her lowest
possible average?
Limits
Derivatives
Applications of
Derivatives
Integration
98
80
87
Applications of
Integration
Integration
Techniques
Series
64
Parametrics
Polar
???
???
85
96
91
Question #6
Amanda has the following
grades on her Calculus
tests this past year. She
can’t remember her grade
on her Parametrics test but
she does remember that her
worst test was Applications
of Integration. She took her
Polar test today but has no
idea how she did on it.
What is the difference
between her highest
possible average for the
year and her lowest
possible average?
Limits
Derivatives
Applications of
Derivatives
Integration
98
80
87
Applications of
Integration
Integration
Techniques
Series
64
Parametrics
Polar
???
???
85
96
91
STOP
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Question #7 time:
Speed answer: 4.5 minutes
Final Answer: 6 minutes
Question #7
The odd positive integers are arranged in
rows in the triangular pattern, as shown.
Determine the row where the number 1001
occurs.
Question #7
The odd positive integers are arranged in
rows in the triangular pattern, as shown.
Determine the row where the number 1001
occurs.
STOP
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Question #8 time:
Speed answer: 2 minutes
Final Answer: 3 minutes
Question #8
Dmitri has a collection of identical cubes. Each
cube is labeled with the integers 1 to 6 as
shown in the following net: (This net can be
folded to make a cube.)
He forms a pyramid by stacking layers of the
cubes on a table, as shown, with the bottom
layer being a 7 by 7 square of cubes.
• Let a be the total number of blocks used.
• When all the visible numbers are added up,
let b be the smallest possible total.
• When all the visible numbers are added from
a bird’s eye view, let c be the largest possible
sum.
Determine the value of a+b+c.
Question #8
Dmitri has a collection of identical cubes. Each
cube is labeled with the integers 1 to 6 as
shown in the following net: (This net can be
folded to make a cube.)
He forms a pyramid by stacking layers of the
cubes on a table, as shown, with the bottom
layer being a 7 by 7 square of cubes.
• Let a be the total number of blocks used.
• When all the visible numbers are added up,
let b be the smallest possible total.
• When all the visible numbers are added from
a bird’s eye view, let c be the largest possible
sum.
Determine the value of a+b+c.
STOP
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Question #9 time:
Speed answer: 3 minutes
Final Answer: 4 minutes
Question #9
A number is Beprisque if it is the only
natural number between a prime
number and a perfect square (e.g. 10 is
Beprisque but 12 is not). Find the sum
of the first five Beprisque numbers
(including 10).
Question #9
A number is Beprisque if it is the only
natural number between a prime
number and a perfect square (e.g. 10 is
Beprisque but 12 is not). Find the sum
of the first five Beprisque numbers
(including 10).
STOP
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Question #10 time:
Speed answer: 4 minutes
Final Answer: 6 minutes
Question #10
Lumba River
Fishing
Felix’s House
Kitty’s House
Felix the cat, wants to give fresh fish to his girlfriend Kitty, as her
birthday present. To do this Felix has to walk to the Lumba River, catch
a bucket of fish and walk to Kitty’s house. The Lumba River is located
105m north of Felix’s house, and runs straight east and west. Kitty’s
house is located 195m south of the Lumba River. If the distance
between Felix’s house and Kitty’s house is 410m, what is the shortest
route that Felix can take from his house to the river and finally to Kitty’s
house?
Question #10
Lumba River
Fishing
Felix’s House
Kitty’s House
Felix the cat, wants to give fresh fish to his girlfriend Kitty, as her
birthday present. To do this Felix has to walk to the Lumba River, catch
a bucket of fish and walk to Kitty’s house. The Lumba River is located
105m north of Felix’s house, and runs straight east and west. Kitty’s
house is located 195m south of the Lumba River. If the distance
between Felix’s house and Kitty’s house is 410m, what is the shortest
route that Felix can take from his house to the river and finally to Kitty’s
house?
STOP
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Question #11 time:
Speed answer: 3 minutes
Final Answer: 4 minutes
Question #11
In a large grassy field
there is a rectangular barn
of dimensions 11m x 5m.
There are 2 horses and a
llama tied to ropes, the
ropes are attached to the
barn at points A, B and C.
The rope at point A is 7 m
long, the rope at point B is
4 m long and the rope at
point C is 5 m long.
Based upon the length of
the rope, in terms of p,
determine the area of
grass that the animals will
be able to reach.
7m
BARN
4m
5m
Question #11
In a large grassy field
there is a rectangular barn
of dimensions 11m x 5m.
There are 2 horses and a
llama tied to ropes, the
ropes are attached to the
barn at points A, B and C.
The rope at point A is 7 m
long, the rope at point B is
4 m long and the rope at
point C is 5 m long.
Based upon the length of
the rope, in terms of p,
determine the area of
grass that the animals will
be able to reach.
7m
BARN
4m
5m
STOP
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Question #12 time:
Speed answer: 3.5 minutes
Final Answer: 5 minutes
Question #12
A palindrome is a positive integer whose
digits are the same when read forwards or
backwards. For example, 2882 is a four-digit
palindrome and 49194 is a five-digit
palindrome. There are pairs of four digit
palindromes whose sum is a five-digit
palindrome. One such pair is 2882 and
9339. How many such pairs are there?
Question #12
A palindrome is a positive integer whose
digits are the same when read forwards or
backwards. For example, 2882 is a four-digit
palindrome and 49194 is a five-digit
palindrome. There are pairs of four digit
palindromes whose sum is a five-digit
palindrome. One such pair is 2882 and
9339. How many such pairs are there?
STOP
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Question #13 time:
Speed answer: 3.5 minutes
Final Answer: 5 minutes
Question #13
•A “double-single” number is a three-digit number
made up of two identical digits followed by a
different digit. For example, 553 is a double-single
number. Let d be the number of double-single
numbers between 100 and 1000?
• Let s be the sum of the digits of the integer equal
to 777 777 777 777 7772 - 222 222 222 222 2232
•Determine the difference between d and s.
Question #13
•A “double-single” number is a three-digit number
made up of two identical digits followed by a
different digit. For example, 553 is a double-single
number. Let d be the number of double-single
numbers between 100 and 1000?
• Let s be the sum of the digits of the integer equal
to 777 777 777 777 7772 - 222 222 222 222 2232
•Determine the difference between d and s.
STOP
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That’s all folks!
Team: _______
Practice Question
Speed Answer:
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Practice Question
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Question #1
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Question #2
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Question #2
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Question #3
Speed Answer:
$5
$25
$125 $625
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Question #3
Final Answer:
$5
$25
$125 $625
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Question #4
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Question #5
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Question #7
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Question #8
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Question #9
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Question #10
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Question #11
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Question #12
Speed Answer:
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Question #13
Speed Answer:
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Question #13
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