BEBRAS 2021 Grade 9-10 Round 2 Ext

The beavers draw three open nine-cell grids. Each cell in the second grid gets one dot; each cell in the third gets two. Letters are entered left to right, top to bottom. A letter is encoded by its cell’s boundary strokes and dots. The key includes examples for A,J,E,Z.



Decode this sequence.

A fairy-tale play has two acts separated by a scene-change break. The figure shows every actor entering and leaving in order. White arrows mean entering; dark arrows mean leaving. Nhà vua=King, Công chúa=Princess, Rồng lửa=Dragon, Hoàng tử=Prince; the rows run from the start of each act to scene change/end.



Which statement is certainly false?

Sue draws a neighborhood whose houses follow a pattern.



Which house belongs in the missing position?

Residents paint houses blue(B),red(R) or green(G). A house must differ from its immediate neighbors on the same side of the street and from the house directly opposite. Some houses have already been painted.



Which colors can the beaver’s house receive?

A musician writes lyrics by following directed arrows from Start. A song finishes at End, but reaching End does not force it to finish immediately: it may continue along an outgoing arrow.



One example song is “Whoop-de-doo lalala Whoop-de-doo La La La Dum-da-da Dum-da-da Bang Dum-da-da Dum-da-da”. Consider these four diagrams.



How many of diagrams 2,3,4 can produce the same lyrics as diagram 1?

Mat invites his friend Robert and two families. The Jones family consists of Papa Jones,Mama Jones,their son Harry and daughter Rose. The Gray family consists of Papa Gray,Mama Gray and daughters Lily,Daisy. Mat wants no two females adjacent, no spouses adjacent, and no child beside either of their own parents. Which circular seating plan works?

Each bucket retains up to its labeled capacity. Extra water is split equally among its outgoing branches. S drains completely; unnumbered terminal buckets collect the incoming water. In the example,200 liters enter S; the 40,20,20-liter buckets finish full, M has 80 liters and N 40.



A different system below starts empty and receives 200 liters through S. No water escapes the system. When flow stops, how much water is in A?

Six islands A,B,C,D,E,F are linked by directed routes. Specialists must travel from A to F to help with an illness, subject to the daily maximum number of people on each route shown.



Travel must follow arrows. What is the largest number of specialists who can reach F on the first day?

The letters I,T,O,C,L are represented by these 3 × 3 black-white grids.



To encode one letter, at each cell count how many of the other four letters have the same color at that position. For example I is encoded as follows.



Which letter gives this numeric table?

Alex has wooden bars of equal height and the illustrated lengths. He wants to use the bars to make three towers of equal height. In each tower, every bar must be strictly shorter than every bar below it. The example illustrates this condition.



For each tower add its bar lengths. The spread is the greatest difference between any two of these three sums. What is the smallest possible spread?

Betty has many cards bearing ABBA,GAGA,GIBB,IGGY. She can place cards consecutively or overlap them; a new card covers the letters underneath. For example: place GIBB; overlap ABBA to get GIABBA; append GAGA to get GIABBAGAGA; overlay IGGY to get GIABIGGYGA. Which string can she certainly not make?

Alex has a wooden box with nine compartments and nine balls. He may choose how many balls to use. Every ball must lie in one compartment, each compartment holds at most one ball, and the number of balls in every row and every column must be odd.



How many different arrangements satisfy all conditions?

A robot starts at the marked entrance and follows the paths. At each fork its controller chooses a branch; at a dead end it collects every gem there. Alex and Bob alternate decisions, Alex first. Alex maximizes the number of gems and Bob minimizes it; both reason perfectly and know the other’s objective.



How many gems will the robot collect?

Sam builds towers from equal-height blocks. Every block within one tower has the same width. He may add or remove blocks to make all towers equally high. Adding or removing one block costs its width in change units; for example two width 1 removals cost 2, and four width 3 additions cost 12.



What is the smallest total change?

There are 16 trees of four different heights, four of each type.



Plant them in a 4 × 4 garden with each type exactly once in every row and column. An outside clue counts visible trees from that direction; a taller tree hides shorter trees behind it. This example illustrates the rule.



Use the clues of this garden.



Which choice gives the tree types at A,B,C,D in that order?