BEBRAS 2019 Grade 9-10 Round 2 Ext

Ada has a box of ten pencils. A box is beautiful when all pencils point in the same direction. In one move she reverses one contiguous group: upward pencils become downward and downward pencils become upward, as in the example.



What is the minimum number of moves needed for this box?

A beaver lives in a small pond, surrounded by forests and rocky regions. The symbols are pond, forest and rock, respectively.







Each day it cuts all forests adjacent to the current pond and turns those regions into pond. Rocky regions cannot be converted.



After how many days will all forests on the map have been cut?

Five directors want as few photographs as possible, with each director appearing in at least one. Their availability and the photographer’s availability are shown.



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 photographs?

Mr Bobby’s class may play football only if all three conditions hold: it is sunny; humidity is low or normal; and no other class has booked the pitch. The forecasts and bookings are below.





Monday: sunny, low, Ms Garcia booked. Tuesday: rainy, high, Mr Smith booked. Wednesday: rainy, normal, free. Thursday: sunny, low, free. Friday: sunny, very high, Ms Parker booked. On which day can they play?

Every dish in the beaver’s recipe book uses exactly four ingredients. It wants two dishes with different tastes. The original table is below.



Egg soup: eggs,onions,chicken,salt. Egg salad: salt,sauce,eggs,onions. Waldorf salad: sauce,walnuts,apples,celery. Pasta: noodles,onions,cheese,tomatoes. Wafers: flour,eggs,sugar,salt. Two dishes have the same taste if they share at least two ingredients, regardless of order. Which pair will certainly not be cooked together?

A pirate’s large square treasure map is divided into small squares. To encode it: (1) represent a uniformly colored region by a square of that color; (2) otherwise draw a circle and divide the region into four quadrants in the illustrated order; (3) repeat until all regions are encoded. The four construction examples establish the quadrant order and sizes.



Here is the pirate’s encoded tree.



Which original map does it encode?

Two beavers must complete eight tasks A(2),B(3),C(5),D(7),E(10),F(9),G(4),H(6); parentheses give hours. Arrows specify prerequisites: E waits for both A and B, F for C, G for D, and H for E.



The source shows a valid 32-hour schedule; Hải ly 1 and Hải ly 2 mean Beaver 1 and Beaver 2.



What is the minimum completion time with two workers?

The family usually arranges one table and chairs as follows.



For larger groups it joins tables in the illustrated way, with examples for two and four tables.



For 35 family members, what is the minimum number of tables using this arrangement?

The source describes “5 towns” along a river, shown below.



Numbers are downstream travel times between consecutive towns. Upstream travel takes 50% longer on each segment; for example town 2→town 1 takes 15 minutes instead of 10. Exactly two towns may receive hospitals. Each resident travels to the hospital taking the least travel time. Where should the hospitals be built to minimize the largest resident travel time?

Editorial clarification: use all six towns numbered 1–6 in the source figure and options; the source’s count “5” is inconsistent with them.

Xavier,Ylenia and Zoe want to reveal whether someone won the lottery while keeping the winner’s identity secret. Each pair meets and tosses one coin. Each person announces whether the two tosses they participated in were the same or different. Everyone tells the truth except a winner, who gives the opposite answer. In this example Zoe won and all announce “different”; Úp and Ngửa label the two coin faces.



Now Xavier says “same”, Ylenia says “same”, and Zoe says “different”. At most one person won. Who is the winner?

A 3 × 5 grid has either a dot or no dot in every cell. The source also states that not every cell contains a dot. Every contiguous 2 × 2 square must contain exactly one or three dots. An example follows.



How many such 3 × 5 grids are there?

A drone photographs objects and rockets from above. A rocket has this 3 × 3 shape.



Because rockets can fly at different heights, their images may overlap other objects. In the photograph, how many possible rockets point north, the direction marked Bắc?

Jin wants a stone bridge home. Pressing a numbered button toggles every cell in that column: a stone disappears and an empty cell gains a stone. A lettered button similarly toggles an entire row. Jin can move between horizontally or vertically adjacent stones, never diagonally.



Hải ly marks Jin beside cell a 5, and Nhà marks home below e 1. What is the minimum number of button presses needed?

Bob drives from Hamper to Mug. Circles mark towns and segments mark two-way roads; each number is the toll charged whenever Bob uses that road. He may change roads at a crossing, but must pay each road’s full toll even if using only part of it. For example B→C can use the roads costing 23 and 6, totaling 29, as indicated.



What is the least possible total toll from Hamper to Mug?

Captain Beaverlian helps according to the priority table: children first, trees second, other work third.



If a new request has lower priority, he continues the current job and postpones the new one. If it has higher priority, he interrupts the current job, completes the new job and then resumes. Equal-priority jobs alternate one hour at a time. The four requests are shown.



Yellow at 9:00: prune trees for 4 hours. Red at 11:00: babysit for 3 hours. Brown at 13:00: dig a tunnel for 1 hour. Green at 15:00: babysit for 1 hour. At what time does Yellow’s request finish?