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BEBRAS 2023 Grade 9-10 Round 2 Ext

Question 1

The commands below change a frog’s color. Each command has the form “If ... then ...” or “If ... then ...; otherwise ...”. Initially the frog has an unknown color. Which commands make the frog blue?

Editorial execution convention: execute the lines in order, testing each condition against the current color after any preceding change. Select all valid options.
  1. If the frog is red, color it blue; otherwise color it yellow.
  2. If the frog is yellow, color it red; otherwise color it blue.
  3. If the frog is yellow, color it red.
    If the frog is not yellow, color it blue.
  4. If the frog is red, color it blue.
    If the frog is not red, color it blue.

Question 2

A maze consists of rectangular rooms and passages as shown.

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Bibako starts at START and follows the direction arrows below to reach Betaro’s room. Which shape is in that room?

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  1. Figure A
  2. Figure B
  3. Figure C
  4. Figure D

Question 3

Bill puts treasure in a maze and sends George the following instruction.

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The source says that George must take 6 steps left, 4 steps right, 1 step left and 2 steps right, and illustrates the following path.

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Which instruction can lead to the treasure along this target path?

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Editorial interpretation: compare the lengths of successive horizontal and vertical runs in the drawings; the source’s direction wording is discussed in the solution.
  1. Figure A
  2. Figure B
  3. Figure C
  4. Figure D

Question 4

A beaver makes decorations from strings and shells. Which decoration below is different from the others?

Question illustration
  1. Figure A
  2. Figure B
  3. Figure C
  4. Figure D

Question 5

The beavers use a secret encoding rule. Someone has decoded part of it and left these clues.

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Which of the four symbol strings is the name of a city in Vietnam?

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  1. Figure A
  2. Figure B
  3. Figure C
  4. Figure D

Question 6

A beaver can follow the arrows through a maze to get home, as in this example.

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In the following maze, however, the arrows would make the beaver get lost. What is the minimum number of arrows that must be changed so it can get home?

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  1. 2
  2. 3
  3. 4
  4. 5

Question 7

A beaver has the four tiles below, each made of unit squares of area 1.

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It wants to place them without overlap in a rectangular box. What is the smallest possible area of the base?

Editorial packing convention: align the tiles with the unit-square grid; rotations by 90° are allowed.
  1. 36
  2. 40
  3. 45
  4. 39

Question 8

Alice encodes each letter as a row of eight colored squares according to a rule. The left example gives A to F, and the right example encodes BEBRAS.

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Which array encodes CHALLENGE using Alice’s rule?

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  1. Figure A
  2. Figure B
  3. Figure C
  4. Figure D

Question 9

Tom uses the following figures to encode letters.

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Each figure and its three successive 90° clockwise rotations correspond, in order, to four consecutive letters of the English alphabet. This example gives the letters encoded by the first figure and its rotations.

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Which string could be encoded by the following sequence?

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  1. COMPUTER
  2. CUSTOMER
  3. COMMERCE
  4. COLONIST

Question 10

Alice, Bob, Chris, Dani and Emily each have a secret number. The five numbers are distinct positive three-digit integers, each using three different digits from 1 to 5.
- If the hundreds digit is 4, the tens digit is not 3.
- The units digits of Alice, Dani and Emily are respectively 5, 2 and 3.
- The hundreds digits of Chris and Emily are respectively 5 and 2.
- If the units digit is 2, the hundreds digit is 4.
- Bob’s tens digit is 2.

Which list, in the order Alice, Bob, Chris, Emily, Dani, could give their numbers?
  1. 531 – 123 – 415 – 342 – 254
  2. 123 – 451 – 234 – 512 – 345
  3. 135 – 321 – 514 – 243 – 452
  4. 543 – 215 – 432 – 154 – 321

Question 11

Beavers A and B chase one another on the following maps. They always stand on black dots. A first jumps to an adjacent dot; then B jumps to an adjacent dot, and they continue alternating. B wins if B jumps onto the dot currently occupied by A. In which case does B have a chance to win?

Question illustration
  1. Figure A
  2. Figure B
  3. Figure C
  4. Figure D

Question 12

Five tasks A,B,C,D,E must be assigned to five beavers, one task to each.
- Beaver 1 can do A or B.
- Beaver 2 can do C or D.
- Beaver 3 can do B or E.
- Beaver 4 can do C or E.
- Beaver 5 can do A, B or D.

How many assignments give each beaver a suitable task?
  1. 2
  2. 3
  3. 4
  4. 5

Question 13

Robots are assembled from a head, body and legs supplied by three conveyors.
- Heads repeat: circle, square, triangle.
- Bodies repeat: blue, yellow, red, purple.
- Legs repeat: one leg, two legs, three legs.

The first robot has a circular head, a blue body and one leg. What does robot number 2022 look like?
  1. Circular head, blue body, one leg.
  2. Circular head, red body, three legs.
  3. Triangular head, yellow body, three legs.
  4. Triangular head, red body, one leg.

Question 14

Sixteen beavers occupy an 8×8 board with two beavers in every row and column.

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Eight beavers can be removed so that exactly one remains in every row and column. In how many ways can those eight beavers be chosen?
  1. 4
  2. 8
  3. 16
  4. 32

Question 15

Three lamps change color continuously according to these repeating rules.
- Lamp I cycles blue, red, purple, yellow, changing every 3 seconds.
- Lamp II cycles blue, purple, yellow, changing every 4 seconds.
- Lamp III alternates blue, red, changing every 5 seconds.

Just now lamps I,II,III have respectively changed to blue,purple,red. How long until their colors are respectively red,purple,blue?
  1. Less than 5 minutes.
  2. About 10–30 minutes.
  3. About 1 hour.
  4. It cannot happen.