Bebras 2021 - Level 1

Four beavers work at a beauty salon: Irina, Ajani, Zuri and Pia. Each is trained to provide hair removal, dental scaling and tail care. These treatments take each beaver 5 minutes, 8 minutes and 15 minutes, respectively. All four start their day at the same time, as shown below. Whoever finishes their current job first will attend to Obi.



Diagram labels: Irina and Pia are doing dental scaling; Zuri is doing hair removal; Ajani is providing tail care.

Which beaver will attend to Obi at the salon?

Ren the beaver may bring a teddy bear to school. The bear must wear a bow tie or a scarf, but must not wear glasses. In addition, there must be exactly one star on the soles of its feet.



How many of the bears shown meet the conditions for Ren to bring to school?

The beaver has a group of alien friends, shown below. Some eat only fish, while others eat only leaves.



The left group eats fish; the right group eats leaves.

Last week, the beaver went out to eat with some friends. The beaver must eat fish if none of the friends in the group eats leaves.



The four groups show Days 1, 2, 3 and 4, from left to right.

On how many of these four days must the beaver eat fish?

The beavers want to complete the railway track so that the train can reach the station.



Which pair of track pieces below can they use, without rotating either piece, to do this?

A museum has four floors. Each floor has seven rooms numbered 1 to 7, as shown below. Some doors connect the rooms.



The plans show Floors 1 and 2 above Floors 3 and 4. “Cửa vào” means entrance and “Lối ra” means exit.

On how many floors can a visitor start at the entrance, visit every room exactly once, and then leave through the exit?

Pierre the beaver lives on island 1 in the picture below. He receives the code “B – A – C – A – A – B”. The code tells him which bridges to cross to reach the hidden treasure.



However, some instructions may not match any bridge available at his current island. Pierre simply skips those instructions. For example, if the instructions are A – B – A and Pierre starts on island 1, he first goes to island 2. Then, since no bridge B is available, he skips that instruction and follows the next instruction by crossing bridge A back to island 1.

On which island will Pierre find the treasure by following his code?

Alex the beaver has five chests labelled with codes, as shown below.



To open them, Alex has five keys labelled with numbers. Identical digits correspond to identical letters, and different digits correspond to different letters.



Unfortunately, the number on one key has disappeared. The picture shows the numbers on the four remaining keys.

Which of the following is the missing number?

The beaver likes collecting stamps and arranging them neatly according to a pattern. Unfortunately, some stamps are missing from the collection below.



Which sequence of stamps correctly fills positions 1, 2, 3 and 4, in that order?

Jan the beaver has a special keyboard. Pressing a key displays a different letter, as indicated by the arrows below.



For example, pressing S displays E, and vice versa.

Which keys must Jan press to display “NOVFIGS”?

The beavers have built a water-purification machine for their city's water supply. To complete the treatment, water must pass through filters N, P and C in that order.



Valve 1 is open and all the other valves are closed. Of valves 2 to 6, how many can the beavers open to be certain that the water coming out has been filtered in the correct sequence?

The beavers use the coding table below to encode letters as special symbols. The table contains the letters A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z in order from left to right and top to bottom. Unfortunately, some symbols in the table are covered.





This sequence of symbols encodes one of the four messages below. What does the message say?

The beaver has nine fir trees of three types (), with three trees of each type. Trees of the same type have the same height; different types have different heights. The nine trees are planted in a 3 × 3 garden so that each type appears exactly once in each row and column.

At each position around the garden, the beaver places a sign showing how many trees can be seen along that row or column. Shorter trees behind taller trees are hidden. The illustration below gives an example of the sign numbers for one arrangement of trees.



Example-picture data, with rows top to bottom and columns left to right:

| Row / Column | 1 | 2 | 3 |
| --- | --- | --- | --- |
| 1 | Short | Tall | Medium |
| 2 | Tall | Medium | Short |
| 3 | Medium | Short | Tall |

Numbers shown in the example:

| Viewing side | Row/column 1 | Row/column 2 | Row/column 3 |
| --- | --- | --- | --- |
| Left (rows) | 2 | 1 | 2 |
| Right (rows) | 2 | 3 | 1 |
| Top (columns) | 2 | 1 | 2 |
| Bottom (columns) | 2 | 3 | 1 |

The following picture gives some of the numbers on the signs around the garden. What is the sum of all the numbers once all signs have been placed?



Clues for the puzzle to solve; — means no number is given, not zero:

| Viewing side | Row/column 1 | Row/column 2 | Row/column 3 |
| --- | --- | --- | --- |
| Left (rows) | 3 | — | — |
| Right (rows) | — | 2 | — |
| Top (columns) | — | — | — |
| Bottom (columns) | 1 | — | — |

The beaver is hungry but is a very picky eater. The decision tree below determines which trees the beaver will eat from.



Diagram labels: “Cây nghiêng sang phải” = tree leans to the right; “Đúng”/check mark = true; “Sai”/cross = false; “Có loại quả chấm bi” = has spotted fruit; “Nhiều hơn 3 quả” = more than 3 fruits; “Ít hơn 3 quả” = fewer than 3 fruits; “Có quả” followed by a fruit picture = has that fruit; “Ít nhất có 1 quả lê” = has at least one pear; “Ăn” = eat. A crossed-out fruit means do not eat.



Which of trees A, B, C, D, E and F might the beaver eat from?

The beavers have the water system shown below. Each bucket holds a fixed maximum amount of water, indicated by the number on it, except for M and N. Any remaining water reaching a bucket is divided equally between its outgoing branches and continues flowing down. At the end, the top bucket S is empty; M and N contain 80 and 40 litres respectively; and all the other buckets contain their full capacities of 40, 20 and 20 litres respectively.



The beavers build a different system, shown below, and pour 200 litres of water into bucket S.



Initially, all buckets are empty, and no water spills out of the system as it flows.

How many litres of water will bucket A contain once the water stops flowing?

Alex the beaver has equal-sized wooden cubes. He uses them to build seven towers, as shown below.



To make all towers the same height, Alex can add cubes or remove cubes already in the towers. Adding or removing one cube counts as one move. For example, changing the leftmost tower's height to 2 takes at least 3 moves, by removing 3 cubes. Changing its height to 7 takes at least 2 moves, by adding 2 cubes. Moving a cube from one tower to another counts as 2 moves.

What is the fewest moves Alex needs to make all the towers the same height?