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?

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?

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?

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?

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?

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?

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.

#

What will the garden look like after this?

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?

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)?

RGB Grid

The RGB colour model is often used in electronics and computing. Squares (often called pixels) are coloured either red, green or blue.

A pattern is used to fully colour an 8 x 11 grid. Part of this colouring is shown below. The pattern is alternating bluegreen in the first row, alternating green-red in the second row, alternating blue-green in the third row, etc.

What coloured squares fit the pattern in the bottom right corner of the grid?

Rivers and Dams

In the Beaver valley, a river splits several times on its way from the source to a nearby lake. Using smartly built dams, the beavers can regulate the amount of water in each arm

of the river for maximum efficiency.

At a fork, the amount of water is divided over the two arms of the river. In the image above,

the amount of water that can flow through the different arms (arrows) per second is shown.

How should the beavers regulate the arms X, Y and Z to get as much water in the

river per second as possible?

Sailing Home

Sailor Beaver is going home. The flag marks the spot where he must drop anchor.

It is getting dark so he wants to get there as quickly as possible by taking the shortest course home but he does not want to crash into the islands. He takes out his compass and plots the course home.

He must follow the shipping lanes, shown as broken lines on the map and he may change direction only on the black dots. He writes down the course he must follow. For example “2N” means go two black dots North, "3SW;2S" means go three black dots South West. Change direction, go 2 black dots South.

His boat is on a black dot as shown on the map. Which instructions will lead the ship to its goal as fast as possible without crashing into an island?

Short story

Here's a short story for you:

"On his way home, Hans finds a cat in front of his house. Because it's raining cats and

dogs, he decides to take it inside. The cat gets comfortable at the chimney and falls

asleep. When Hans' mother arrives home, she accidentally bumps into the cat. The cat

gets scared and scratches her leg."

This story can be summarised using abbreviations. Everything that can't be shortened, is left out.

Sorting tree trunks

Robot Alan is sorting tree trunks. Unfortunately, we forgot how he was programmed exactly.

On the ground, there are several tree trunks of different lengths.

Alan chooses a tree trunk following a certain formula, lays it on top of the ramp and lets it roll down.

He repeats this, until there are no more tree trunks on the ground.

See the result:

Which formula does Alan use to decide in which order the tree trunks have to be placed on the ramp?