Bebras 2014

Islands and bridges

The settlements of the Beavers are divided over different islands. They want to build

bridges, so trading goods will become easier. Beaver Beatrix has made a plan, which you can see below. The islands are represented by dots, the bridges by lines.

The other beavers would prefer a different plan though, on which the islands are

represented by lines and the bridges by dots.

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Log Jam

The beavers collected 50 logs on Beaver Island. They want to bring these logs to

their home through the river system. At various points in the river system, they lose a certain number of logs. The beavers begin on Beaver Island (at the left side of the diagram) and wish to get home (which is on the right side of the diagram). On the river there are numbers, which show how many logs the beavers would lose, if the beavers use this river on their route home.

What is the fewest logs the beavers could lose?

• 20 logs

• 23 logs

• 15 logs

• 19 logs

Mirrored or not?

Sandy and her friend Horatio got new computers last week.

The computers have a built-in camera at the top of the screen.

When Sandy is chatting with her friend, the chatting software has two windows: a big one which is showing Horatio chatting and a small one showing herself chatting. The chatting software has two possible settings for showing the video streams:

"mirror mode" - right eye on the right side of the screen and "picture mode" - right eye on the left side of the screen. Look at this picture of Sandy and Horatio chatting:

Which settings does the chatting software have on Sandy's computer?

• Sandy's video stream in picture mode Horatio's video stream in picture mode

• Sandy's video stream in picture mode Horatio's video stream in mirror mode

• Sandy's video stream in mirror mode Horatio's video stream in picture mode

• Sandy's video stream in mirror mode Horatio's video stream in mirror mode

Missing piece

Beaver Bruce has received a secret message sent on a 6 x 6 grid. Unfortunately, part of

the message has been destroyed by a spill of red juice.

This case was foreseen (Bruce spills a lot of juice) and there are additional squares in the message that can help Bruce determine the secret message. Each square in the rightmost column (column 6) is coloured such that the number of black squares in each row is even. Similarly, each square in the bottommost row (row 6) is coloured such that the number of black squares in each column is even. Which of the following images could be the pattern

underneath the red spill?

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Neighbourhoods

Neighbourhoods in areas on maps can be presented as a diagram. In such a neighbourhood

diagram each neighbourhood is represented by a node.

A line between two nodes means that the two neighbourhoods share one or more borders.

The diagram on the right shows the connections between seven neighbourhoods in a certain area.

Which of the following maps is described by this diagram?

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No Anonymity Anymore

The medical records of patients contain personal data, which should not be made public.

For the publication of a research project, the hospital has made some data public, without

mentioning the names of the patients. The table on the left shows a part of this list.

Because of the upcoming elections, the city with postcode M1 1AA publishes a list with all

constituents at the same time. This table on the right shows the constituents who are born on January 1st.

Thanks to these two tables, you know for sure that one of the persons on the right has a

disease and you also know which disease it is.

What is the name of this person?

• George Smiths

• Roman Petersons

• Eve Miller

• Isabele Bourne

Packing Logs

Beatrix has a backpack that holds a maximum of 7 kg of wood. Large 3 kg logs are worth 5 coins each. Medium 2 kg logs are worth 3 coins each. Small 1 kg logs are worth half a coin. How many logs of each size should Beatrix pack in her backpack to maximise the total worth?

• One large logs and two medium logs

• Two large logs and one small logs

• Three medium logs and one small logs

• one large logs, one medium logs, and three small logs

Planting Flowers

A big and a small beaver are planting flowers in the garden. The small beaver has shorter arms and legs than the big beaver. Therefore, his steps are smaller and the flowers he plants are closer to each other.

The beavers start back to back and are looking in opposite directions.

They both follow these directions:

Repeat two times:

Plant a flower on your right

Go one step forward

Plant a flower on your left

Go one step forward.

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What will the garden look like after this?

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Playing Cards

The beavers want to make playing cards out of five pieces of cardboard.

The pieces of cardboard have different sizes: A4, A5, A6, A7 and A8.

A4 is twice as big as A5, A5 is twice as big as A6 and so on.

They need 12 playing cards of size A8 and they don't want to waste any paper.

Which pieces of cardboard should they use?

• A4 and A5

• A6 and A7

• A5 And A6

• It is not possible

Programmed Robot

A robot is programmed to find a target (the green field marked with X) on a map of square

fields. The robot has its movements programmed as follows:

• The robot moves straight forward until it reaches an obstacle (black field) or the edge of the map.

• When reaching an obstacle or the edge of the map, the robot turns right by 90°.

• When the robot moves out of a field, the field becomes a black obstacle.

The arrows on the maps below show the starting position as well as the starting direction of the robot.

On which map does the robot NOT eventually reach the target (green field marked with X)?

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