Bebras A 2014

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?

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?

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?

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.

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