BEBRAS 2026 Grade 11-12 Round 2 Ext

A beaver encodes letter strings using shapes. The examples show corresponding words and symbols.



What message does the following symbol string represent?

Saro wants to pick apples using a ladder that is safe only for people weighing at most 50 kg. The table lists friends' heights in centimetres and weights in kilograms.



The names are Batin, Tamin, Lamin, Asin, Babin; their heights are 155,150,168,145,155 cm and their weights are 52,50,55,40,48 kg in that order. Who is the tallest friend who can use the ladder safely?

A knight encrypts messages by replacing each English letter with the letter three places later, wrapping around: a→d, b→e,...,x→a,y→b,z→c.



For example “Ave Cesar” becomes “Dyh Fhvdu”. What was the original meaning of “L dp lq wkh pdunhw”?

A beaver needs a wrench to tighten a nut. Ten wrenches are arranged from smallest to largest, and exactly one fits.



What is the least number of trials that guarantees finding the correct wrench?

Editorial convention: a trial reveals too small, fits, or too large; if only one candidate remains, identifying it by elimination counts as finding it without an additional physical trial.

A robot plants a row of flowers according to the signs, starting at X.



Repeat steps 1–5 until no signs remain:
1. If the current cell has a sign, plant the flower shown there.
2. Remember the flower just planted.
3. Remove the current sign.
4. Move right until reaching an empty cell with neither a flower nor a sign; plant the remembered flower there.
5. Move left until reaching a cell with a sign or leaving the bed.

What will the final flowerbed look like?

A beaver and a bear cut long logs into pieces. The beaver makes one cut per minute. The bear has two saws and can simultaneously make two cuts 1 metre apart. They may work at the same time, but not on the same log. Each cutting operation takes one minute. A beaver can split 7 m into 1 m and 6 m; a bear can split 7 m into 2 m,1 m,4 m.







The beaver alone loads 7 metres of finished pieces onto the truck per minute; the bear cannot help load. Today there are three 7-metre logs, to be made into nine 1-metre pieces, three 2-metre pieces and two 3-metre pieces. What is the shortest total cutting-and-loading time?

Editorial scheduling convention: each loading operation occupies the beaver for one full minute and loads up to 7 metres of pieces already finished before that operation begins. Cutting and loading cannot overlap for the beaver.

A car park has four sections: A only for people with disabilities, B only for teachers, C only for parents, and D for everyone. A person may qualify for several sections; for example a parent can use C or D. Initially A,B,C,D have 3,1,3,2 empty spaces. Five cars arrive in order: teacher 1 (with a disability), teacher 2, teacher 3, parent 1, parent 2. Nobody leaves. Four proposed remaining-capacity rows are shown.



In English, “Khả năng” means possibility; the rows for A,B,C,D are (2,1,0,1), (2,1,1,0), (3,0,1,0), (3,0,0,1). How many possibilities can occur?

A beaver currency exchange trades coins for branches of different sizes. To minimize the number carried, each customer wants as few branches as possible. Branch prices are shown; each size has unlimited supply.



Four customers have 15,16,17,18 coins respectively and exchange the full amount. What are their respective minimum branch counts?

A translation system supports languages A,B,C,D,E. Its accuracy for each pair lies between 0.0 and 1.0, with larger values better, as in the table.



Accuracy through intermediate languages is the product of the accuracies used. For example C→A has accuracy 0.2, while C→B→A gives 0.5×0.9=0.45>0.2. Consider A→D, B→A, C→B and D→B. For how many can an indirect translation be strictly more accurate than the direct one?

Min encodes a row of black/white cells recursively:
- If all cells in the current row are white, write W.
- If all are black, write B.
- Otherwise write X, then encode the left half by the same rules, followed by the right half.

Here are examples.



What is the encoding of this row?

A beaver encodes letters using arrangements of stones and sticks, as shown.



With 17 stones and 16 sticks, what is the greatest number of letters that can be formed?

A secret computer uses binary strings. Rule 1: five bits represent 0–31, with place values 16,8,4,2,1 from left to right. The examples are 00001=1, 00101=4+1=5, 11111=16+8+4+2+1=31.



Rule 2: assign A–Z the numbers 1–26 and encode with five bits, for example A=1 (00001), B=2 (00010), C=3 (00011), Z=26 (11010). Rule 3: prefix 0 for a letter or 1 for a number, making each symbol six bits. Thus 000001 means letter A, while 100001 means number 1. What does the 18-bit string 000011100100000010 mean?

Bob's mosaic uses grey or white shapes described as having 3,4,5 or 6 vertices. In every row and every column, both the number of white shapes and the total vertex count are odd. A wave replaced exactly two original shapes. The damaged mosaic is shown.



These five loose pieces were found nearby.



Which two are the original pieces that were replaced?

Editorial counting convention: count a star's five outer tips as 5 for this puzzle, rather than its ten boundary vertices. The five labelled loose pieces are individual objects, each usable at most once.

Seven ponds hold 9,4,1,5,3,2,6 units of water after heavy rain. To avoid flooding, all water must reach the main reservoir, directly or through other ponds. The dashed arrows are proposed pipes; each number is both the pipe's safe capacity and its construction cost.



“Hồ chứa chính” means main reservoir. What is the minimum total cost of a safe pipe system carrying all water to it?

Four one-way tram lines run as shown.



Line A departs A every 3 minutes; B departs B every 2; C departs C every 4; D departs D every 5. Their first departures of the day are simultaneous. Edge numbers are travel times in minutes between circular stops; stopping time is negligible. Passengers may transfer at common stops, sometimes waiting for the next tram. Marcus wants the fastest route from home to the theatre (“Rạp hát”). How many stops does he pass, including A and the theatre stop, and what is the minimum time?

Editorial timing convention: Marcus boards the first A departure at the common start time, taken as minute 0.