Part A
Two teams are playing baseball. To keep track of their score, each team uses helmets and a row of hooks. The rightmost hook represents a score of 1 and each other hook represents twice the value of the hook to its right, as shown.
(image found in Google slide)
Each hook can have at most 1 helmet, and the total score for a team is the sum of all the scores on the hooks with helmets. For example, the following row of hooks would represent a score of 16 + 4 = 20.
(image found in Google slide)
What is the difference between the two scores?
(A) 11
(B) 9
(C) 13
(D) 7
(A) 11
Emil's friends have each recorded different data about all the tree species in a forest. When Emil has a question while hiking in the forest, he knows he can call these friends to find the answer to his question.
Severin records the shape of the leaf for each tree species.
(Image in Google slides)
Quirina records the fruit as well as whether or not the tree has cones for each tree species.
(Image in Google slides)
Ladina records each tree species along with the colour of its bark and whether or not its wood is suitable for building a beaver lodge.
(Image in Google slides)
Emil has found a leaf. He wants to know if it belongs to a tree species whose wood is suitable for building a beaver lodge. Which of his friends must he call?
(A) Only Ladina
(B) Only Severin and Quirina
(C) Only Severin and Ladina
(D) Severin, Quirina and Ladina
(C) Only Severin and Ladina
Sofia has 15 programmable lights of three types: , , and . She numbers them from 1 to 15 and connects them in a star shape as shown.
Hide/Reveal Description of Diagram for Lights
Each light is controlled with a switch and Sofia programs the other lights as follows:
Each light turns on if the two lower-numbered lights connected to it are both on.
Each light turns on if exactly one of the two lower-numbered lights connected to it is on. In other words, one of these lower-numbered lights is on but the other is not.
Question
All the lights are off and then Sofia turns on lights 1, 2, and 4 at the same time. Which of the five lights closest to the centre (lights 11, 12, 13, 14, and 15) will turn on?
(A) Lights 11, 12, 13, 14, and 15
(B) Only lights 12, 13, and 15
(C) Only lights 11, 12, 13, and 14
(D) Only lights 11, 13, and 14
(D) Only lights 11, 13, and 14
Aira is walking from her house to her friend Bo's house for the first time. A map of the streets between their houses is shown. All streets go either east/west or north/south.
(Image in Google slides)
Bo gave Aira the following instructions, where walking one block means walking straight until you reach the next street.
However, Aira made a mistake with one of the steps and did not arrive at Bo's house. Her route is shown.
(Image in Google slides)
Which step did Aira not follow correctly?
(A) Step 1
(B) Step 2
(C) Step 3
(D) Step 4
(B) Step 2
A magician can transform one type of fruit into another. The magical transformations are denoted by M. The fruit that the transformation is applied to is put inside brackets and the fruit that the transformation produces is put on the right after an equals sign. Six magical transformations are shown in the table below. For example, the top-left entry in the table describes a magical transformation that can be applied to an to produce a .
Transformations can be combined. For example, since we know
M()=
we can write the following combined transformation:
M(M())=M()=
What fruit is produced by the following combined magical transformation?
M(M(M(M(M( )))))
(A) Image in Google slide
(B) Image in Google slide
(C) Image in Google slide
(D) Image in Google slide
(B)
The arrangement below uses light blue and dark grey shapes. Each shape has 3, 4, 5, or 6 outer points.
A grumpy beaver didn't like the arrangement above. So, at two locations it removed the shape and then replaced it with a different shape. After doing this, every row and every column had:
an odd number of light blue shapes, and
an odd number of total outer points.
Question
Which of the following two new shapes might the beaver have used?
(A)
(B)
(C)
(D)
(A)
Seven planes are lined up for take-off using a single shared runway. A plane cannot take off if there is a plane waiting directly in front of it.
(Image in Google slides)
The following table shows the take-off schedule, but some of the planes are missing from the schedule.
(Image in Google slides)
(D)
Hermit crabs wear shells in order to protect themselves. As hermit crabs grow, their shells become too small and the hermit crabs need to look for larger shells to wear.
An assortment of new shells has just been washed ashore. Several hermit crabs have gathered to try on these new shells. In the following diagram, the letters represent the hermit crabs and the numbers represent the new shells. A single line connecting a letter to a number means that the hermit crab has determined that the shell is a good fit. If there is no line connecting a letter to a number then the hermit crab has determined that the shell is not a good fit.
Question
If a shell can only be worn by one hermit crab, and a hermit crab can only wear one shell, then what is the maximum number of hermit crabs that can wear one of these new shells?
(A) 8
(B) 7
(C) 6
(D) 5
(B) 7
Sarah has a very specific procedure for describing sequences of black and white squares:
If all the squares of a sequence are white, she writes to describe the sequence.
If all the squares of a sequence are black, she writes to describe the sequence.
Otherwise, to describe the sequence, she writes , and then
follows her procedure for describing the left half of the sequence, and after it is complete,
follows her procedure for describing the right half of the sequence.
Below are four examples of sequences and what Sarah writes to describe each of them using her procedure.
SequenceDescription
Question
What does Sarah write when using her procedure to describe the following sequence?
(A) XXXWBWXBXBW
(B) XXXWBXWWXXBBXBW
(C) XWBWXBBW
(D) XXXBWBXWXWB
(A) XXXWBWXBXBW
Apples , bananas and pears are placed in five baskets so that each basket has eight pieces of fruit.
Given any two baskets, Blake always prefers the basket with more apples. If two baskets have the same number of apples, then Blake prefers the basket with more bananas.
Which of the following shows the five baskets ordered from Blake's most preferred to least preferred from left to right?
(Image in Google slides)
(D)
In the land of Bebravia, there are six towns. All food is grown in Quandaria and transported by train to the other towns. The train routes are indicated by lines drawn between towns in the diagram. The arrow on each line indicates the direction in which trains carrying food are allowed to move.
Bebravia is not large so there is more than enough time for many trains to travel between any two towns. The only limitation is the daily capacity on each train route: the number on each line indicates the maximum number of trains that can travel along that route on one day.
Question
In one day, what is the largest number of trains that can travel from Quandaria to Pixleton?
(A) 13
(B) 16
(C) 19
(D) 12
(A) 13
Marcus wants to go from his home to the theatre by bus. The following map shows Marcus's home, the theatre, and four bus lines with circles representing bus stops.
Each bus departs from the top of the map. The first bus on each of the four lines departs at the same time. After that, buses depart on each line at the time intervals shown in the squares. For example, a bus departs on the orange line leaving Marcus's home every 3 minutes.
Each line segment between two bus stops is labeled with the number of minutes it takes to travel between the two stops. For simplicity, assume that stopping at a bus stop to load and unload passengers takes no time (0 minutes).
Stops with two or more bus lines intersecting can be used to change buses. If Marcus arrives at an intersection point, he can change to a bus that arrives there at the same time or later.
Question
If Marcus departs on the first bus closest to his home, what is the shortest time, in minutes, needed for him to reach the theatre?
(A) 18
(B) 19
(C) 20
(D) 21
(C) 20