WorksheetsBebras A 2014
Total questions: 15
Worksheet time: 45mins
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 log and two medium logs
Two large logs and one small log
Three medium logs and one small log
one large log, two medium logs and one small log
Stage Coaches
In the Wild West, where the cowboy beavers live, the Bebras Stage Coach Company built a network of stage coach routes between eight settlements.
In the plan of transportation, you can see at which days of the week the stage coaches will depart at the different settlements. A stage coach departs early in the morning and arrives at the next settlement in the evening of the same day.
What is the fastest way to get a package from settlement 1 to settlement 8?
1-2-5-8
1-3-6-8
1-2-6-8
1-4-7-8
Turning numbers
In the game of "Turning Numbers" you can scramble the numbers 1 to 9.
At the start of every game, the numbers are orientated as shown in the picture on the left.
When you push button A, B, C or D, the numbers around make a quarter turn.
For example: when you push button A, the numbers will be placed as shown in the image on the right side.
You start a new round and push the following buttons:
D, C, B, B.
Where will the number 4 be at the end?
Turning Glasses
There are five drinking glasses on the table. One of them is turned upside down.
In this game, you have to get all glasses upright again. But: you have to turn exactly three glasses every turn.
How many turns do you need at least to get all the glasses standing upright?
2 turns
5 turns
3 turns
impossible
Vigenère encryption
Beavers Beatrix and Bruce encrypt their private messages, so others cannot read them. They use the same key for encrypting and decrypting the messages.
The key they use is CAB.
Beatrix encrypts a message to Bruce:
Because the C is the third letter in the alphabet, the first letter in the message (W) is replaced by the letter which comes three places after it in the alphabet (Z). Because the A is the first letter in the alphabet, the second letter in the message (H) is replaced by the letter which comes one place after it in the alphabet (I). And so on, until the complete message has been encrypted.
Bruce
answers: DUGOFXHO
When do they meet?
(a)
Watering a tree
The beaver has made a pipe system for watering his apple tree.
Valves 1, 2, 3 and 4 can be opened or closed independently.
In which case does the water reach the
apple tree?
Valve 1 closed 2 opened 3 closed 4 closed
Valve 1 opened 2 closed 3 closed 4 opened
Valve 1 opened 2 opened 3 closed 4 closed
Valve 1 closed 2 closed 3 closed 4 opened
Wood streams
In forest (A) is an area where the beavers fell trees for their dams. They transport the tree
trunks to their new project - the biggest dam of all times (D) - through an infrastructure of
channels. The arrows represent the channels, the dots are points where the water splits up or comes together. Every channel has a restricted capacity. The numbers next to the channels show how many tree trunks can be transported through the channels in one minute.
How many tree trunks can be transported from A to D at most in one minute?
(a)
The Wrong Hat
Anna, Bert, David and Emily Beaver have two rules for choosing what clothes to wear:
• Normally, they wear a hat of their favourite colour.
• They wear a shirt with a different colour than the hat.
One day, they change hats, just for fun. Now they all wear a hat of another colour than
their favourite one.
Which beaver owns the green hat?
(a)
Tic tac toe
You are playing a game of tic-tac-toe with your friend. First your friend has to place an 'O', then
you place your 'X'. You continue taking turns in this way. The player who places their three
marks in a horizontal, vertical or diagonal line wins.
It is your turn to put an 'X' in the grid below:
Click on the grid to place your 'X’ so that you have the best chance of winning.
(a)
Toothbrushes
It is time for bed! Every beaver should have a toothbrush that matches their size. But look at the picture to see what has happened. “Not so fast!” sighs mother beaver. “Eve and Chad, swap your brushes! Ann and Chad, you too!” But then she does not know how to continue.
Which two beavers still need to swap their toothbrushes so that all the beavers have
the correct brushes?
Ben and Chad
Ann and Eve
Ben and Dan
Nobody
Storm proof network
On a small green island a network of mobile phone towers is setup. Every tower covers a circular area of the island. When the coverage area of two towers overlaps the towers are said to be directly connected. Towers can also be indirectly connected if there is a chain of directly connected towers between the two towers.
The operators want to make the network of towers Storm Proof. This means that even if one tower breaks down all other towers must still be connected, either directly or indirectly. Which system shown below is a way to create a storm proof network on the island?
Space maze
Some space explorers landed on an empty planet. From their ship they could see a maze with
an unknown golden object in it. The explorers dropped their robot into the maze hoping it could take a closer look at the unknown object. Unfortunately the robot broke during the fall and can now only send and receive garbled instruction about where to go. The robot suggests four possible directions it can go. Even though the words in the instructions are garbled, there are still only four different words, each indicating north, west, east or south.
When following the instructions the robot will move into an adjacent square as instructed.
Which instructions should the explorers send the robot in order for it to reach the
golden object?
Ha' poS poS Ha' Ha' nIH
Ha' poS poS Ha' nIH Ha'
Ha' Ha' poS Ha'
Ha' poS nIH vI'ogh Ha' poS
Alice and Tom are playing a game of "True or False" on their colourful, magnetic whiteboard in their classroom. Alice has stuck seven different magnetic shapes on the board. She then makes four statements about the shape, colour, size and position of the shapes. Only one statement is allowed to be true. Tom must figure out which one it is. Which of the following statements is true?
There are two shapes X and Y, so that X is dark blue and Y is pale yellow and X is higher than Y.
For all pairs of shapes X and Y, if X is a square and Y is a circle, then X is higher than Y.
For all pairs of shapes X and Y, if X is small and Y is big, then X is to the right of Y.
For all pairs of shapes X and Y, if X if light yellow and Y is dark blue, then X is below Y.
Height game
Young beavers Amy, Beavy, Cuttree, Diggy and Eary, want to play a game with you. They all stand in a line. Then they each count how many beavers are taller than they are both infront of them and behind. They give you the results on a slip of paper: In what order are the beavers standing?
Diggy, Cuttree, Amy, Beavy, Eary
Amy, Cuttree, Diggy, Eary, Beavy
Diggy, Amy, Cuttree, Beavy, Eary
Diggy, Amy, Eary, Beavy, Cuttree
Meeting point
Three friends Anne, Bernie and Clara live in a city with an underground train system. The map of the system below shows the stations and connections between the stations. The map also indicates how many minutes each connection takes. Anne lives next to Ashbourne station, Bernie's nearest station is Best, and Clara's is Corner. They wish to select a station for a meeting. None of the friends should take more than 15 minutes of travel to reach the meeting point.
Which stations qualify as possible meeting points?
Ashbourne and Corner
Ashbourne and Park
Park and Outbound
Park and Upleft
