BEBRAS 2023 Grade 7-8 Round 2 Ext

A robot bee executes commands one at a time: the straight arrow moves one square forward in its current direction; the right-turn and left-turn symbols rotate it in place without moving.



The examples illustrate a right turn and a forward move.



The bee is now in the bottom middle square facing upward, with its hive in the upper left square.



Which command sequence brings it to the hive?

To draw on a square grid, start at the gray square and move in one of eight directions numbered as shown: 0 east, 1 northeast, 2 north, 3 northwest, 4 west, 5 southwest, 6 south, 7 southeast.



The example shows the start, the sequence 1,0,0,7,7,5,5,4,3,3,2 and the resulting shaded squares.



Beaver wants to draw the following shape from its starred square.



Which movement sequences draw it? Select all valid options.

Nam, Việt, Mai and Mi each wear a hat, shirt and shoes in blue, red, purple or yellow. No two children have the same hat color, shirt color or shoe color.



The table columns are Name / Hat / Shirt / Shoes. Nam: blue / yellow / red. Việt: yellow / blue / purple. Mai: red / purple / yellow. Mi: unknown in all three columns. What colors are Mi’s hat, shirt and shoes?

Each beaver holds a number card. They sort themselves into increasing order from left to right. Compare the first two beavers and swap them if the first number is larger. Then compare the second and third, then the third and fourth, and so on. After the rightmost pair, restart from the left. Stop only after a full pass with no swap. The example sorts 8,5,4.



Starting with the five beavers below, how many swaps are needed?

Bob designs a robot beaver that follows these commands.



English translation: Tx = go to location x; G = pick up wood; D = put down wood. For example, T4T2GT4D sends the robot to the bridge, then location 2, to pick up wood, back to the bridge, and to put down the wood. The robot works in this forest:



Which program collects the wood at locations 1, 2 and 3 and puts it at location 5? To cross the river, the robot must use the bridge.

Tortoise and Hare start together at the heart and run along the arrows. Each arrow is one step.



Tortoise moves one step per minute; Hare moves twice as fast, two steps per minute. At which pictured position do they first meet again?

The bee enters at the left arrow and leaves at the right arrow. It visits each hexagonal cell at most once, collecting the amount of honey printed there, then moves to an adjacent cell in one of the six indicated directions.



It cannot enter either striped cell. What is the greatest total honey it can collect?

Alex makes strings from striped and plain beads. Start with a striped bead followed by a plain bead.



At each step choose either (i) add one plain bead to each end, or (ii) append two striped beads to the right end. These steps may be repeated.



How many of the following four strings can Alex create?

Every year, the beavers choose a “lucky queen” as follows:
- Each participant receives a letter card. They stand clockwise in consecutive letter order around a circle.
- Starting with A, they count 1, 2, 3 clockwise. Anyone who says 3 is eliminated; the next remaining beaver restarts at 1. Continue until one remains.
- The last remaining beaver is the lucky queen.
This illustrates the case of four participants:



What if there are ten participants holding A, B, C, D, E, F, G, H, I, J?



Who becomes the lucky queen?

Eight trees are planted in a circle. Last week Alice stood inside it and took a complete 360° panorama as shown.



Today she takes another panorama and finds that two trees have been cut down. Which photograph could she take?
Option A:



Option B:



Option C:



Option D:

Beaver must distribute five items among Fuzzy, Wuzzy and Izzy. Each person values each item differently, as shown.



Columns mean Item 1, Item 2, Item 3, Item 4, Item 5. Fuzzy’s values are 10, 13, 8, 5, 3; Wuzzy’s are 2, 11, 4, 5, 6; Izzy’s are 6, 10, 6, 4, 8. For example, Fuzzy values item 1 at 10 units, while Izzy values it at only 6 units. If Wuzzy has items 4 and 5, Wuzzy has 11 units of value. Beaver A envies Beaver B if A considers B’s items to have greater total value than A’s own items. All five items must be distributed so that no one envies anyone else. What total value could Fuzzy receive? Select all valid options.

In COL, two players take turns placing their own pieces on empty vertices of the pictured board. One plays white and the other gray. A player loses if two of their own pieces occupy vertices joined by a line. The example shows White losing.



In the following current position, where should White play to guarantee victory?

Tom uses the following figures to encode letters.



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.



Which string could be encoded by the following sequence?

Beaver is in a two-floor maze. On either floor, moving between edge-adjacent cells takes one second if no thick wall blocks the move. Switching magically to the corresponding cell on the other floor takes five seconds.



“Tầng 1” and “Tầng 2” mean Floor 1 and Floor 2. For example, from A it can move down or left in one second, or switch to C on Floor 2 in five seconds. What is the shortest time from A to B?

Two beavers play five rounds of darts with these rules:
- Each player throws three darts per round.
- The player with the dart nearest the center wins that round. The winner scores 1, 2 or 3 points according to how many of their darts are closer to the center than the opponent’s nearest dart.
The diagram shows all five rounds and the first-round scores.



“Lượt” means “Round”; “điểm” means “points”; A scores 1 and B scores 0 in round 1. What is the combined total score of the two players after five rounds?