June 2021
©2021 University of Waterloo
Question | Answer |
---|---|
1 | 7.5 |
2 | 3 cm |
3 | 30 |
4 | 29 |
5 | 125 |
6 | |
7 | 7 |
8 | 6 |
9 | |
10 | (17,4) |
11 | B, C, E |
12 | 5 |
13 | 172 |
14 | 4 |
15 | 60 |
5 | 7 | B | 3 | 1 | B | 6 | 2 | 1 |
1 | B | 1 | B | 6 | 5 | 4 | B | 5 |
7 | 3 | 1 | B | 4 | B | 6 | 2 | B |
B | 6 | B | B | 4 | B | B | B | 6 |
2 | 0 | 5 | 5 | B | 1 | 1 | 2 | 8 |
4 | B | B | B | 1 | B | B | 5 | B |
B | 4 | 3 | B | 0 | B | 1 | 8 | 1 |
3 | B | 8 | 5 | 2 | B | 9 | B | 4 |
2 | 0 | 4 | B | 9 | 3 | B | 4 | 7 |
Position in Photo | |||||
---|---|---|---|---|---|
1 | 2 | 3 | 4 | ||
Location | Park | Blanche | Dorothy | Rose | Sophia |
Kitchen | Blanche | Dorothy | Rose | Sophia | |
Garden | Rose | Sophia | Dorothy | Blanche | |
Driveway | Blanche | Dorothy | Sophia | Rose | |
Basement | Blanche | Sophia | Dorothy | Rose |
Player | Player 1 | Player 2 | Player 3 | Player 4 |
---|---|---|---|---|
Correct Answer | 5 | 3 | 17 | 24 |
Player | Player 1 | Player 2 | Player 3 | Player 4 |
---|---|---|---|---|
Correct Answer | 110 | 165 | 101 | 808 |
Player | Player 1 | Player 2 | Player 3 | Player 4 |
---|---|---|---|---|
Correct Answer | 9 | 6 | 50 | 138 |
Player | Player 1 | Player 2 | Player 3 | Player 4 |
---|---|---|---|---|
Correct Answer | 5 | 13 | 57 | 228 |
From the graph, we can see that Ana spent
Answer:
Since the four sides of a square are equal in length and the
perimeter is
Answer:
If the symbol
Answer:
The character starts by moving
Inside the loop, the character moves
In total, the character has moved
Answer:
Since
Answer:
Exactly
Answer:
Recall that a prime number is an integer greater than 1 whose
only divisors are
The prime numbers between
Thus, there are
Answer:
Every triangular prism has exactly
Answer:
The pattern repeats after every .
Answer:
We start by reflecting the lizard over the dotted line as shown.
We then translate the lizard 7 units to the right, as shown.
The tail now has coordinates
Answer:
It is possible to trace over all the lines exactly once in Picture B, Picture C and Picture E.
First we will look at Picture B.
One way to do trace all the lines as described is to start from Dot 1 and trace over the line connecting Dot 1 to Dot 2 and then trace over all the remaining lines, finishing at Dot 2.
There are other ways to do this, but the important thing is that we have to start at either Dot 1 or Dot 2 since these are the only dots with an odd number of lines coming out of them. Every time we pass through a dot (other than at the beginning or end), we use up an even number of lines. So, the only way to use up all the lines for a dot with an odd number of lines coming out of it is to make sure that dot is the first or last dot.
Notice that Picture C and Picture E each have exactly two dots with an odd number of edges coming out of them. We can trace over all the lines exactly once in each of these pictures by starting at one of these dots and finishing at the other.
Picture A and Picture D each have more than two dots with an odd number of lines coming out them, so there’s no way to trace over all the lines in these pictures exactly once.
Therefore, it is possible to trace over every line, as described, in Pictures B, C, and E.
Answer: B, C, E
Since the known numbers in the list are all different, then if
the unknown number is different than each of these, there is no single
mode. Therefore, the unknown number must be equal to one of the known
numbers. It follows that the unknown number will also be the mode.
If we arrange the known numbers in increasing order, we have:
If the unknown number is
If the unknown number is
If the unknown number is
Therefore, the unknown number is
Answer:
We begin by considering the positive integers between
The next
Answer:
Bea, Diane, and Gene have each met
Edgar and Foster have both met
Amad has met
Cho has met
Therefore, Hans has met
Answer:
Since the robot must travel though
We begin by considering the following three paths from
Notice that these paths involve two moves right and three moves down.
In fact, every path from
Counting the number of different possible sequences of moves, we
get:
There are a total of
Similarly, we can consider the following two paths from
Notice that these paths involve five moves right and one move down.
In fact, every path from
There are a total of
We now consider three of the possible paths from
Notice that, in each of these three paths, the robot takes the same
path from
Answer:
5 | 7 | B | 3 | 1 | B | 6 | 2 | 1 |
1 | B | 1 | B | 6 | 5 | 4 | B | 5 |
7 | 3 | 1 | B | 4 | B | 6 | 2 | B |
B | 6 | B | B | 4 | B | B | B | 6 |
2 | 0 | 5 | 5 | B | 1 | 1 | 2 | 8 |
4 | B | B | B | 1 | B | B | 5 | B |
B | 4 | 3 | B | 0 | B | 1 | 8 | 1 |
3 | B | 8 | 5 | 2 | B | 9 | B | 4 |
2 | 0 | 4 | B | 9 | 3 | B | 4 | 7 |
The range is
Since
From the grid, the hundreds digit of this number is
The sum is
July and August each have
The result is
The product is
From the grid, the ones digit of this number is
From the grid, the ones digit of this number is
From the grid, the hundreds digit is
A dozen is a set of
The sum of the digits in this number must be
From the grid, the tens digit of this number is
The smallest prime number greater than
The number is
The number is
The digits are determined from the clues to
An odd multiple of
A rectangle with area
In a square, each angle is equal to
The number is
From the grid, the tens digit of this number is
The digits of
Since
Then
The mean is
The number is
There are
The value is
Start by considering the second, eighth and first clues (in that order).
(2) Dorothy and Sophia are the only people to ever stand in Position 2.
Although we do not yet know which person occupies which Position 2 in each photo, we can make note that one of them does.
(8) The order for the garden photo is the reverse of the order for the driveway photo.
Since either Dorothy or Sophia occupy the second position in these photos, it follows that they must occupy the third position as well. As a result, Blanche and Rose must somehow occupy Positions 1 and 4 in these photos.
(1) Blanche is standing in Position 1 in four of the five photos.
Since the garden photo is the reverse of the driveway photo it is not possible for Blanche to be in Position 1 in both of these photos. Thus, in order to be standing in Position 1 in four photos, she must be standing in Position 1 in the park, kitchen and basement photos. Then, the fourth photo with Blanche in Position 1 will be either the garden or driveway photo.
The following partially-completed table contains what we have determined from these three clues.
Position in Photo | |||||
---|---|---|---|---|---|
1 | 2 | 3 | 4 | ||
Location | Park | Blanche | Dorothy/ Sophia |
||
Kitchen | Blanche | Dorothy/ Sophia |
|||
Garden | Blanche/ Rose |
Dorothy/ Sophia |
Dorothy/ Sophia |
Blanche/ Rose |
|
Driveway | Blanche/ Rose |
Dorothy/ Sophia |
Dorothy/ Sophia |
Blanche/ Rose |
|
Basement | Blanche | Dorothy/ Sophia |
Next, we consider the third clue.
(3) Rose is standing in the same position for the photos in the basement and the driveway, but she isn’t standing in that position in any other photos.
We previously determined that Rose is standing in either Position 1 or Position 4 for the driveway photo. Since she must be standing in the same position for the basement photo it follows that she must be standing in Position 1 or Position 4 in the basement photo. But, Blanche is standing in Position 1 in the basement photo, and so Rose must be standing in Position 4 for both the basement and the driveway photos.
Now that we know Rose is standing in Position 4 in the driveway photo, we also know that Blanche is in Position 1. Furthermore, since the garden photo is the reverse of the driveway photo, we know that in the garden photo Rose is in Position 1 and Blanche is in Position 4.
Furthermore, since Rose is not standing in the same position in the park and kitchen photos as she is in the driveway/basement photos, it follows that Rose is not standing in Position 4 in either the park or the kitchen photos. We already know that Blanche is in Position 1 in both photos, and that either Dorothy or Sophia are in Position 2 in both photos. Therefore, Rose must be standing in Position 3 for both the park and the kitchen photos.
Position in Photo | |||||
---|---|---|---|---|---|
1 | 2 | 3 | 4 | ||
Location | Park | Blanche | Dorothy/ Sophia |
Rose | |
Kitchen | Blanche | Dorothy/ Sophia |
Rose | ||
Garden | Rose | Dorothy/ Sophia |
Dorothy/ Sophia |
Blanche | |
Driveway | Blanche | Dorothy/ Sophia |
Dorothy/ Sophia |
Rose | |
Basement | Blanche | Dorothy/ Sophia |
Rose |
Now, we consider the fourth clue.
(4) Dorothy is never standing in Position 1 or Position 4.
In both the park and the kitchen photo, the only possible positions left for Dorothy to stand in are Positions 2 and 4. Since Dorothy can never stand in Position 4, she must be standing in Position 2 for both of these photos. This leaves Sophia standing in Position 4 for both the park and the kitchen photos.
Position in Photo | |||||
---|---|---|---|---|---|
1 | 2 | 3 | 4 | ||
Location | Park | Blanche | Dorothy | Rose | Sophia |
Kitchen | Blanche | Dorothy | Rose | Sophia | |
Garden | Rose | Dorothy/ Sophia |
Dorothy/ Sophia |
Blanche | |
Driveway | Blanche | Dorothy/ Sophia |
Dorothy/ Sophia |
Rose | |
Basement | Blanche | Dorothy/ Sophia |
Rose |
Notice that we have now determined the order in which the siblings are standing for the park and kitchen photos. That means, that the sixth clue is not actually needed. But, we can confirm that it is in fact satisfied, since the siblings are standing in the same order for the park and kitchen photos.
Now, we can use the fifth clue.
(5) Sophia is standing in Position 2 exactly twice.
Since the garden photo is the reverse of the driveway photo, Sophia is in Position 2 exactly once in these two photos. As a result, to be in Position 2 exactly twice, she must be in Position 2 in the basement photo. As a result, Dorothy must be standing in Position 3 in the basement photo.
Position in Photo | |||||
---|---|---|---|---|---|
1 | 2 | 3 | 4 | ||
Location | Park | Blanche | Dorothy | Rose | Sophia |
Kitchen | Blanche | Dorothy | Rose | Sophia | |
Garden | Rose | Dorothy/ Sophia |
Dorothy/ Sophia |
Blanche | |
Driveway | Blanche | Dorothy/ Sophia |
Dorothy/ Sophia |
Rose | |
Basement | Blanche | Sophia | Dorothy | Rose |
Finally, the seventh clue tells us where Dorothy and Sophia are standing in the garden and driveway photos.
(7) In three of the four photos where Blanche is standing in Position 1, Dorothy is standing next to her.
This clue is equivalent to saying that in three of the four photos where Blanche is standing in Position 1, Dorothy is standing in Position 2. Currently, we have determined that Dorothy is standing in Position 2 in exactly two photos where Blanche is standing in Position 1. Therefore, Dorothy must be standing in Position 2 in the driveway photo (where Blanche is standing in Position 1). As a result, Sophia will be standing in Position 3.
Since the garden photo is the reverse of the driveway photo, we know that in the garden photo Sophia is in Position 2 and Dorothy is in Position 3. This completes the logic puzzle.
Position in Photo | |||||
---|---|---|---|---|---|
1 | 2 | 3 | 4 | ||
Location | Park | Blanche | Dorothy | Rose | Sophia |
Kitchen | Blanche | Dorothy | Rose | Sophia | |
Garden | Rose | Sophia | Dorothy | Blanche | |
Driveway | Blanche | Dorothy | Sophia | Rose | |
Basement | Blanche | Sophia | Dorothy | Rose |
(Note: Where possible, the solutions are written as if the value of
P1: Evaluating,
P2: The numbers
Since the answer to the previous question is
P3: The sum of the side lengths is
Since the answer to the previous question is
P4: Since
Since the answer to the previous question is
Answer:
P1: A vertical line can be drawn to separate the shape into two
rectangles. One rectangle has an area of
P2: If
Since the answer to the previous question is
P3: In increasing order, the known numbers are:
If
If
If
Since the answer from the previous question is
P4: If there were
Since the answer from the previous question is
Answer:
P1: There are
P2: In total, Pierre has
When divided among
Since the answer from the previous question is
P3: The terms in this sequence are:
Since the answer from the previous question is
P4: There are
There are
The total length of rope, in cm, is
Since the answer from the previous question is
Answer:
P1: The numbers less than
P2: We can remove one square from each side of the balance so we
are left with two triangles and one square on the left side, and one
circle on the right side.
Now, the mass of one circle is equal to the mass of two triangles and
one square, or
Since the answer from the previous question is
P3: In
Since the answer from the previous question is
P4: Each time Fatemah writes the sentence, she writes the letter
"S"
Since the answer to the previous question is
Answer: