BEBRAS 2024 Grade 7-8 Round 2 Ext

The three maps show different features of the same village, with the same scale and north direction: forest in gray, river in gray, and houses as squares.



Karla lives in a house that is in the forest and next to the river. Which numbered house is hers?

The city uses the letters in this table. Gray cells are consonants; white cells are vowels.



Each four-character identification code begins with a digit 0–9. Each of the other three characters must be a letter from the table; the second character must be a vowel and the last must be a consonant. Consider TAA8,5ATO,1UEK,3OOP,6KTS,9UTU,4AOG,3I9K,2OPR. How many are valid?

Saud encodes letters using the row-and-column symbols in this table.



Which message could the following sequence encode?

Beaver moves from START to STOP through the grid. At each step Beaver may move to the immediately adjacent cell on the right or immediately below, if it exists.



Each cell’s number is the energy consumed when passing through it. What is the least total energy Beaver can consume on the journey?

Paint spreads each second from colored cells to edge-adjacent cells, but cannot cross walls. The example shows the initial state and the states after one and two seconds.



How many seconds are needed to color every cell of this maze?

In the morning Alice, Bob and Tom arrange wooden letters as LEAVES.



On each later visit Alice removes one letter, Bob inserts one letter anywhere, or Tom replaces one letter by another. They may visit repeatedly.



By evening the word is BLUEBERRIES.



What is the minimum total number of visits after the morning meeting?

The city has four kinds of banknote shown here.



Cells are numbered left to right, top to bottom.



For example, cells 1,2,6 distinguish the notes as shown; “Ô” means cell and “Kết luận” means conclusion.



It is also possible to distinguish all four notes by looking at just two cells. If their numbers sum to S, what is the remainder when S is divided by 4?

Beaver uses a rule to encode letters as strokes. The first three drawings encode ELEMENT, BEAVERS and BANANAS.



Which listed word could the remaining drawing encode?

Ben uses the right-hand rule: on entering a maze, he keeps his right hand against the wall on his right throughout the walk. This does not necessarily visit every part of a maze. Starting at each entrance arrow and stopping at the exit, in which maze does the walk visit every part?

The robot starts in the bottom-left cell and must reach the gray top-right cell.



U moves up one cell, R right one cell, and D down one cell. It can remember at most five commands and repeat the same group as often as needed. Which listed group reaches the target with the fewest entries into white cells?

Each construction piece has four features: width, height, number of protruding connectors and number of indented connectors. Three pieces may share a bag if, for each feature separately, all three values are equal or all three are pairwise different. The example has equal widths, three different heights, protrusion counts 1,0,2 and indentation counts 2,1,0.



How many different triples can be selected from these nine pieces?

The academy selects athletes by four criteria:1 plays more than three sports;2 runs 100 metres within 30 seconds;3 is the best player in some sport;4 jumps farther than one metre. Each criterion has a weight, and an athlete is selected when their total weight is strictly greater than a threshold. For example weights 1,4,2,3 and threshold 6 select someone satisfying criteria 2 and 4 because 4+3=7>6. In this recruitment only Bob and Tom are selected. The table shows which criteria each applicant meets.



Rows are criteria 1–4; Alex meets 3,4; Bob 1,2; David 1,4; Henry 2,3; Tom 1,3. Which weights for criteria 1,2,3,4 could produce this result?

A printer repeats this pair of actions three times: print a square of any size anywhere, then print a circle of any size anywhere. Later shapes cover earlier shapes where they overlap. How many of the four pictured results are certainly impossible?

Eight teams 1–8 play a knockout tournament. Winners advance and losers are eliminated, according to this bracket.



Labels mean Round 1,Round 2,Round 3 and Tournament winner. After completion each empty box contains the winning team’s number. Four observers count how many times each team number appears in the completed bracket, including the original leaves.



The table rows are teams 1–8 and columns Andy,Beth,Cece,Daniel. Exactly one observer is correct. Who?

Every cell is gray or white. Every minute all cells update simultaneously using their eight surrounding neighbors, including diagonal neighbors: a gray cell with fewer than 2 gray neighbors becomes white; with 2 or 3 it stays gray; with more than 3 it becomes white. A white cell with exactly 3 gray neighbors becomes gray. Otherwise its color stays unchanged. The example shows one minute.



Starting with this board, how many gray cells remain after two minutes?