BEBRAS 2017 Grade 3-4 Round 2 Ext

A mouse wants to reach the cheese at the bottom of pipe 5. It always goes down, and at every side junction it switches to the neighbouring pipe.



Which entrance should it use?

Here is a lock.



Which key can open it?

Beatrix arranges her shelf by two rules: rectangular objects cannot be next to each other, and round objects cannot be next to rectangular objects. Which shelf obeys both rules?

A train delivers materials to three towns along the railway, in this order: Timber needs wood, Hay needs straw, and Wall needs bricks.



How should the wagons be attached to deliver in that order?

Theseas descends from Mount Troodos to the Soleas valley, collecting the number of pieces of wood written at each station. He may travel only downward along the shown links, never climb back up.



What is the greatest amount of wood he can collect?

Bill stores words in a 100-page dictionary. Add the alphabet positions of the letters, add 1, then subtract the number of letters to get the page. For example BAY gives 2+1+25+1-3=25.



He stores BEAVER, FUR, TAIL, TEETH and WOOD. Which listed page contains the most words?

Four guests each bring one gift. Each gives a gift to one other guest, each receives exactly one gift, and nobody gives to themselves. Art→Bran means Art gives to Bran; Art→Bran, Cáit→Art describes two gifts.



Which arrangement obeys the rules?

Explorer Bob finds the cave exit blocked by these rocks.



One punch destroys a striped rock; a checkered rock needs two punches, becoming striped after the first.



A rock falls when both rocks supporting it have been destroyed.



Bob escapes after 8 punches. Which picture shows the exit then?

Bony receives a cryptex which opens when its discs spell the password. It has six independently turning discs, not five as in this illustrative photograph. Each carries the English alphabet and can turn only forwards through alphabet order, wrapping after Z.



Starting at SECRET, rotate disc 1 by 13 letters, disc 2 by 13, disc 3 by 24, disc 4 by 21, and disc 6 by 10. What is the password?

Benno turns 11 today, but his mother has only five birthday candles. She puts them in a row. The rightmost lit candle has value 1; moving one place left doubles the value, so the second has value 2. Add the values of all lit candles: the rightmost two together give 2+1=3.



Which lighting pattern represents 11?

Firefighter Frank recruits volunteers in Beaverville. The map shows homes and the roads directly connecting them. Every home must either contain a volunteer or be exactly one road away from a volunteer’s home.



What is the fewest volunteers needed?

Benno makes Schoggimousse for the family and needs five eggs of equal weight. Of six eggs, five weigh the same and one is heavier. A balance scale shows only which side is heavier or whether they balance; several eggs may be placed on a pan.



What is the fewest weighings that guarantees finding the heavier egg?

The beaver doctor wants three health stations. From every labelled location, a beaver must be able to reach a station by swimming through at most one canal.



Which set of locations should be chosen?

A beaver and friends use a shared Internet cable along poles, as shown. One break, perhaps caused by a fallen tree, stops the beaver’s Internet connection. The beaver can ping a computer’s IP address from the map. For example: ping 2001:db8::ff00:42:8329. A reply such as “64 bytes from 2001:db8::ff00:42:8329, time=22.9 m” means that computer is still reachable; “100% packet loss, time 999 ms” means the cable is broken somewhere before it.



What is the fewest ping commands needed to guarantee locating the broken segment?

Buddy decorates a tree with four bows and fourteen balls. Prices in beaver dollars label the ornaments. Dashed lines lead left and solid lines lead right; for example 100,70,30,10,12 form one linked route. A tree is pretty if, for every ornament, prices in its left branch are smaller and prices in its right branch are larger. It is colourful if it is pretty, the top ornament is a ball, and every bow has two immediate ball children.



Which description is correct?