BEBRAS 2019 Grade 5-6 Round 2 Ext

Mawar plays a ring-toss game. On each turn she tries to throw a ring around the pole, as shown.



She throws five rings in order. A successful first throw earns 5 points, second 4, third 3, fourth 2 and fifth 1, according to the table.



How many points does she earn if the final arrangement is as follows?

World-famous chemist Maja wants to obtain as many new compounds as possible. Initially she has A, D and E. She can perform these experiments:
1. B, C and D produce A and F.
2. D and E produce A, E and F.
3. A and C produce B and D.
4. A and F produce B.
Which is the largest set of compound types she can obtain?

Five company directors want souvenir photographs with each director appearing in at least one photo. To save money, they want as few photos as possible. Their availability and the photographer’s are shown.



English translation: Alam 15:00–17:05; Bob 12:00–16:00; Cecilia 13:00–14:05; Denise 14:00–17:05; Erik 17:00–18:00; photographer 12:00–20:00. What is the minimum number of photos?

Beaver Chef finds a cookbook in which every dish uses exactly four ingredients. He wants two differently flavored dishes for dinner, selected from this table.



English translation:
- Egg soup: egg, onion, chicken, salt.
- Egg salad: salt, sauce, egg, onion.
- Waldrof salad: sauce, walnut, apple, celery.
- Spaghetti: pasta, onion, cheese, tomato.
- Sponge cake: flour, egg, sugar, salt.
Two dishes count as the same flavor if they share at least two ingredients, in any order. Which pair will definitely not be cooked together?

Beaver words obey these rules:
- They use only these three symbols.



- Reading left to right or right to left gives the same word. Examples:



- A word’s length is its number of symbols. This word has length 3:



How many words of length 3 can be formed?

Each beaver arranges seven white or gray bottles from left to right, following these rules:
- The third bottle must be gray.
- If a gray bottle is placed, all bottles after it must also be gray, if any.
Their arrangements are shown.



Which beavers did not follow the rules?
Editorial note: the printed choices do not provide a complete answer under the literal rules. Automatic grading is disabled; see the explanation.

Henry is an expert on locks. He discovers how keys and locks work, as shown in this example before and after insertion.



He then makes this key:



Which lock below can it open?

Ada has ten pens in a box. She calls the box beautiful if all pens point the same way. In one move she may reverse any consecutive group: upward pens become downward and downward pens become upward, as in this example.



What is the minimum number of moves to make this box beautiful?

Beavers A, B, C and D each inspect one of the town’s four dams. Their wages are 1 coin per meter from home to the assigned dam. The distances are shown.



English table: columns are dams 1,2,3,4; A:185,145,143,190 m; B:130,125,175,225 m; C:50,50,100,75 m; D:220,186,185,225 m. What is the minimum total wage?

Editorial assignment convention: each dam is inspected by exactly one beaver.

Judy likes camping with her family. She takes different equipment depending on the place.



English translation: park = racket and baseball glove; mountain = tent and cap; sea = tent and swim ring; river = racket and swim ring. Equipment is kept in a store. After each trip, the used items are placed above the items still in storage, as in the park example.



Now compare the storage order before and after two trips.



Which two places did the family visit recently?

Table-heading translations: Before going to the park / Park trip / After going to the park; Before two camping trips / Two camping trips / After two camping trips.

Two beavers plan to meet in this maze.
- They alternate jumps, with the female beaver going first.
- A jump follows the arrow in the current cell for the number of cells written there.
- They meet if they occupy the same cell.



After how many steps will they meet?

Color some arrows in this diagram so that:
- Each uncolored arrow points toward exactly one other uncolored arrow.
- Each colored arrow points toward exactly two other colored arrows.



How many arrows are colored?
Editorial clarification of “points toward”: count every arrow along the indicated straight ray, not only the nearest arrow.

Aqil secretly hides a toy car under one of four numbered boxes.



Aidel must find it using Aqil’s code. Digits are read in pairs: for example, 1324 first swaps positions 1 and 3, so each becomes the other’s new position; then it swaps positions 2 and 4 in the same way. Aqil starts with the car under box 3 and gives this code:

1234132414231234

Under which numbered position should Aidel look?

Roni forgot the three-digit password to the treasure cave, but wrote these clues:
- The password has three digits.
- 1 7 2 contains exactly one correct digit, in the wrong position.
- 8 5 4 contains exactly two correct digits, both in wrong positions.
- 9 8 6 contains exactly one correct digit, in the wrong position.
- 7 5 1 contains exactly one correct digit, in the correct position.
What is the sum of the password’s digits?

Two beavers build a dam by completing eight tasks: A(2), B(3), C(5), D(7), E(10), F(9), G(4), H(6), where each number is the task’s duration in hours. Some tasks must wait for others, as the arrows show.



English diagram labels: Start and Finish mark the overall project. E waits for both A and B; H waits for E; F waits for C; G waits for D. Here is one schedule taking 32 hours:



The rows are Beaver 1 and Beaver 2; gray blocks are idle time. What is the shortest possible completion time?