COMPUTATIONAL &
ALGORITHMIC THINKING
Intermediate Years 9 & 10
(Australian school years)
TUESDAY 2 APRIL 2019
NAME:
INSTRUCTIONS
•
Do not open the CAT paper until told to do so.
•
Maintain silence at all times.
•
Do not bring mobile phones into the room.
•
You may use calculators and printed language dictionaries.
•
You may NOT borrow equipment without a supervisor’s permission.
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There are 9 questions. Questions 1–6 are multiple-choice with five possible answers given.
Questions 7–9 (each with three parts) require a three-digit answer. Attempt all questions.
Penalties do not apply.
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You are allowed working time of one hour (60 minutes). There is no extra reading time.
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Diagrams are NOT drawn to scale. They are intended only as aids.
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The questions have been thoroughly checked. Each question stands as written.
No further explanation of questions can be provided.
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You must not leave your seat. If you have any other questions or problems, please raise
your hand and wait for a supervisor.
•
If you wish to leave the room a supervisor must accompany you.
•
Record all your answers on the answer sheet provided.
•
Use B or 2B lead pencils only. Ball point and ink pen markings may not activate the
optical scanner.
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Do not make any other marks on the answer sheet as these may make the sheet unreadable.
•
If you make an error, use a plastic eraser to completely remove all lead marks and smudges.
•
Check the number of the answer you are filling in is the same as the number of the question
you are answering. This is particularly important if you decide to leave a question blank.
•
To ensure the integrity of the CAT and to identify outstanding students, the AMT
reserves the right to re-examine students before deciding whether to grant official status
to their score.
Reminder: You may sit this competition once, in one division only, or risk no score.
Copyright © 2019 Australian Mathematics Trust AMTT Limited ACN 083 950 341
2019 CAT — Intermediate
Computational and Algorithmic Thinking 2019 (Intermediate)
1
Part A: Questions 1–6
Each question should be answered by a single choice from A to E.
Questions are worth 3 points each.
1. Greg Value
The Greg value of a number can be found by adding all the digits in an even position
and subtracting all the digits in an odd position.
For example, the Greg value of 4 5 6 8 3 2 is (5 + 8 + 2) − (4 + 6 + 3) = 2.
A 12-digit number is to be formed by arranging these four cards:
216
432
412
317
What is the largest Greg value that can be obtained?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 10
2. Hearts / Spades
You have a line of cards consisting of hearts ♥ on one side and spades ♠ on the other.
You are allowed to choose a card and flip that card and all of the cards to the right of it.
For instance, if you chose the 4th card in the next line you would flip the rightmost 6
cards:
♥ ♥ ♠ ♠ ♥ ♥ ♠ ♠ ♠ −→
♥ ♥ ♠ ♥ ♠ ♠ ♥ ♥ ♥
The line of cards below has 8 ♥s and 7 ♠s.
♥ ♥ ♠ ♠ ♥ ♥ ♥ ♠ ♠ ♥ ♠ ♠ ♠ ♥ ♥
How many cards should you flip to get the greatest number of ♠s in the line?
(A) 1, 2 or 3
(B) 4, 5 or 6
(D) 10, 11 or 12
(C) 6, 8 or 9
(E) 13, 14 or 15
2019 CAT — Intermediate
Computational and Algorithmic Thinking 2019 (Intermediate)
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3. Wetlands
All of the swamps in the wetlands are empty! The wetlands consist of 10 swamps as
shown in the map. The numbers represent the capacities in megalitres (ML) of the
swamps. The arrows show the direction that water can flow along a channel connecting
two swamps.
10
5
100
20
20
15
10
5
10
15
5
One hundred ML is being pumped into the leftmost swamp. Once a swamp is filled, any
excess flows to the next swamps, dividing equally when there is more than one channel.
How many ML of water will flow into the rightmost swamp?
(A) 0
(B) 5
(C) 10
(D) 15
(E) 20
2019 CAT — Intermediate
Computational and Algorithmic Thinking 2019 (Intermediate)
3
4. Annoying Nephew
You are looking after a rather annoying nephew for the afternoon, and the internet is
down. So you devise a task for him. You draw the following circle.
C
D
A
A
C
→ D
clockwise
E
A
anticlockwise
B
E
A
D
Then you put a counter on the D at the leftmost part of the circle. You tell him to follow
these rules.
1. If the counter is on an A, move it clockwise 1 position.
2. If the counter is on a B, move it clockwise 4 positions.
3. If the counter is on a C, move it clockwise 2 positions.
4. If the counter is on a D, move it to directly opposite its current position.
5. If the counter is on an E, move it anticlockwise 2 positions.
You then ask him where the counter would be after 607 moves.
Which letter would the counter be on?
(A) A
(B) B
(C) C
(D) D
(E) E
5. Magician
Five cards labelled A, B, C, D and E are in a pile on a table in some order.
1. A magician takes the top card and places it at the bottom of the pile.
2. He then takes the next card and lays it on the table to form the beginning of a row.
3. He then takes the next card and places it at the bottom of the pile.
4. He then takes the next card and places it at the right end of the row.
5. He repeats steps 3 and 4 until he has all the cards in the row.
If they are now in the order A B C D E, what was the bottom card in the original pile?
(A) A
(B) B
(C) C
(D) D
(E) E
2019 CAT — Intermediate
Computational and Algorithmic Thinking 2019 (Intermediate)
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6. Add Ten
Flow diagrams provide a visual way of showing a process or algorithm: a box is used
for an action, a diamond (shaded) for making a decision, and arrows indicate the flow
of control.
Each of the values 36, 77, 357, and 11498 in turn is input to the flow diagram below.
Input A
Set B to 0
Is B < A?
yes
Add 10 to B
no
Set C to 0
Is A = B?
no
Add 1 to C
Subtract 1 from B
yes
Output C
How many of the outputs are less than 5?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
2019 CAT — Intermediate
Computational and Algorithmic Thinking 2019 (Intermediate)
5
Part B: Questions 7–9
Each question has three parts, each of which is worth 2 points.
Each part should be answered by a number in the range 0–999.
7. Landscaping
Your landscaping company has teams of workers. When a job involves mowing and
pruning, half of the team mow and the other half prune. For each worker of a team, you
know how much profit they will make if they mow, and how much they make when they
prune.
For instance, suppose there were four workers in a team and the profits for assigning
each to mowing or pruning were
Worker 1 2 3 4
Mowing 5 2 6 5
Pruning 3 4 3 5
Then the most profit ($20) would be made by assigning the first and third workers to
mowing and the other two to pruning.
For each of the following teams, what is the most profit you could make if half of the
team was assigned to mowing and the remainder to pruning?
A.
B.
C.
Worker
Mowing
Pruning
1
3
4
2
2
2
3
4
3
4
4
2
5
3
5
6
6
3
7
3
4
8
1
2
Worker
Mowing
Pruning
1
2
3
2
3
3
3
4
3
4
5
4
5
4
5
6
1
2
7
4
6
8
2
3
9
3
5
10
4
4
Worker
Mowing
Pruning
1
6
7
2
8
7
3
5
4
4
2
1
5
4
1
6
0
2
7
3
2
8
1
2
9
5
3
10
1
3
11
15
14
12
6
4
2019 CAT — Intermediate
Computational and Algorithmic Thinking 2019 (Intermediate)
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8. Inertia
Astrid the astronaut is floating in a grid. Each time she pushes off she keeps gliding
until she collides with a solid wall, marked by a thicker line. From such a wall she can
propel herself either parallel or perpendicular to the wall, but always travelling directly
←, →, ↑, ↓. Floating out of the grid means death.
Y
*
Y
X
*
*
In this grid, Astrid can reach
square Y from square . But if
she starts from square there is no
wall to stop her and she will float
past Y and out of the grid.
In this grid, from square X Astrid can float to
three different squares with one push (each is
marked with an *). Push ← is not possible from
X due to the solid wall to the left. From X it
takes three pushes to stop safely at square Y,
namely ↓ → ↑. The sequence ↑ → would have
Astrid float past Y and out of the grid.
In each of the following grids, what is the least number of pushes that Astrid can make
to safely travel from X to Y?
A.
Y
X
2019 CAT — Intermediate
Computational and Algorithmic Thinking 2019 (Intermediate)
7
B.
Y
X
C.
X
Y
9. Caravanserai
You have to travel by camel train from Uktu to Timb. You
will need to stop overnight at a number of caravanserais on
the way. The camels will bypass one caravanserai but not
two on the one day. At each caravanserai, you have to pay
for lodging. Each caravanserai charges a different cost.
You do not mind how long the journey takes, but you want
to pay as little as possible for lodging.
Each of the following lists gives the cost of lodging at a chain of caravanserais between
Uktu and Timb. For each, what is the least total cost of lodging on your journey?
A.
175681
B. 5 7 3 4 9 5 4 6
C.
543844721
1
D
2
A
3
C
4
E
5
D
6
E
7A
31
7B
39
7C
60
8A
5
8B
6
8C
4
9A
13
9B
20
9C
17
INTERMEDIATE
Intermediate
ANSWER KEY
Question