Claire wants to make a necklace for her mum.

She has a certain way to bead her hand-crafted necklace, which is illustrated in the following picture.

All possible necklaces that can be produced by Claire are described by this picture.

Claire is always taking the beads following the arrows in the picture.

The following necklace could be made by Claire.

What necklace could be made by Claire too?

(A)
(B)
(C)
(D)

John wants to take a trip to visit nine cities of his country: Onecity, Twocity, Threecity, Fourcity, Fivecity, Sixcity, Sevencity, Eightcity and Ninecity.

There are bus lines connecting some of these cities.

The buses make the following routes in both directions:

• Threecity - Onecity
• Ninecity - Twocity
• Threecity - Ninecity
• Ninecity - Onecity
• Onecity - Twocity
• Sevencity - Eightcity
• Eightcity - Sixcity
• Sixcity - Fivecity
• Fivecity - Fourcity
• Fourcity - Sevencity

Bertie the bee has to work fast and fill honey pot to take to the market.

Which vent pipes must be open to make Bertie reaches pot in the shortest way?

Sally the snake is coming up with a dance.

Which image comes next in the dance?

(A)
(B)
(C)
(D)

Beaver Ivan bought a new yellow robot car.

The car moves by executing a given list of commands.

For example, the list

leads him from his home (at the bottom left corner) to the barbershop:

The car cannot cross solid lines !

Which list of commands leads beaver Ivan from his home to the gas station ?

(A)
(B)
(C)
(D)

Grandpa beaver cannot use computers very well.

He is asked to create a password for his e-mail account.

This password has to:

• be longer than 5 characters (letters or numbers or special characters) and
• have at least 2 special characters: *, #, /, +

Which password would be accepted by the computer?

Next to you there is a basket full of apples of different sizes.

Step 1: You take an apple out of the basket and put it on the table in front of you.

Step 2: You reach for the next apple out of the basket and execute the following comparisons.

C1: If the apple in your hand is smaller than the one on the table, then you put the apple from your hand into the other basket.

C2: If the apple in your hand is larger than the one on the table, then you put the apple on the table into the other basket and put the apple
from your hand on the table.

You repeat step 2 until the initial basket is empty.

Which of the following is always TRUE about the apple that remains on the table at the end?

An artist printed four identical copies of a picture on clear film so that each copy can be viewed from all sides.

A forger paints a copy of this picture and also prints the fake on clear film.

He then exchanges one of the four original copies with his fake one.

Which one is the fake copy?

(A)
(B)
(C)
(D)

Any even length string with equal left and right halves are called tandem or repetition.

For example, both ABAB and POPPOP are tandems.

Beaver Alex looks at fragment of his friend Vlad DNA string.

For analyzing this fragment he must find longest tandem substring.

Help him to find it.

DNA fragment is AACGTACGTACCTTACTAC.

What is the maximal length of tandem substring?

Two beavers are having a dance-off.

Each will respond to the crowd's different type of cheering and perform a specific dance move.

They perform their moves simultaneously one square at a time in the direction corresponding to the arrows below.

The following table depicts how the two competitors will move:

So for example, if the crowd cheers "Roar!", Justin will move one square right then one square down and simultaneously, Selena will more one square up and one square to the left.

They start on the dance floor as follows:

Which of the following sequences of cheers will cause the two to finish on the same square?

Granpa beaver cannot use computers very well. 

He is asked to create a password for his e-mail account.

This password must comply to the following rules.

• At least 2 capital letters
• More letters than numbers
• At least 3 special characters (not a letter and not a number)

Which password would be accepted by the computer?

Traffic jam in a city!

It is impossible to turn left in such a traffic density.

My father is hurrying up home by car from the hotel he works.

In the picture below the travel duration for each street in minutes is given.

What is the least possible time taken, in minutes, to go from the hotel to his home when it is not possible to turn left?

The beavers are hospitable and they like visit each other.

However, sometimes they are not at home.

Therefore, they need to leave a message for their guests using an informational gate.

The beavers has come up with 4 different messages, as follows:

	We are at home. Please come in.
	We will come back at noon.
	We will come back in the evening.
	We will be back at midnight.

However, Little Beaver Cheolsoo thinks it is possible to make up more than 4 messages by changing the place of these logs.

He knows that the logs must meet the following conditions:

– The logs can only either be attached horizontally, or be removed completely.
– The shape and orientation of the logs are not important.

But he does not know exactly how many messages are possible.

What is the maximum number of messages that are possible, including the 4 original messages?

The beavers have made a code that uses the map above:

• Every tree in the park is named with a letter.
• The code for each letter is found by how to get to its tree by turning left and right.
• The code for each letter always starts from the park entrance.

Example 1: The code for A is LL because to get to tree A from the park entrance you must turn left twice.

Example 2: The code for the word BAR is LRLLLR.

How many letters are there in the beaver’s code for the word BEAR?

There are 12 spaces for cars in a parking lot.

Each space is labelled with a number.

The pictures below show which spaces were used on Monday and which spaces were used on Tuesday.

Parking lot on Monday:

Parking lot on Tuesday:

How many parking spaces were empty on both Monday and Tuesday?