Anja uses acorns, stones, a strawberry and pearls, together with sticks, to make the network shown below.
The rule for making the network is: “The two ends of each stick must have two different objects.” Unfortunately, a beaver has eaten the strawberry. Anja must quickly put an object in the strawberry’s place and remove one stick to satisfy the rule. Which picture below could show the network after Anja repairs it?
A family consisting of a father, mother, older sister and younger brother prepares breakfast for the next day in four stacked boxes, each containing one kind of fruit.
In the morning, each person takes the top box and carries it to work.
The mother always wakes up first and the father last. Their preferences are shown below, where 0 means dislike and 1 means like.
One day, thieves stole gold from the Beaver Bank and hid it in 3 of the 8 houses shown below.
The police quickly investigated. One officer found out exactly which houses contained gold. He sent his colleague a message of eight digits using 1s and 0s: 1 represents a house containing gold, and 0 represents a house without gold.
A rabbit lives in house A. It wants to collect all the carrots on the roads shown below.
It takes 1 minute to travel along each road between any two of the points A, B, C, D and E. How many minutes does the rabbit need to leave home, collect every carrot, and return home?
A beaver designs a ball-collecting robot using the following steps:
The diagram reads: Start → Wait for a ball to fall onto the floor → Go to the ball → Pick up the ball → Go to the basket → Put the ball in the basket → Wait for a ball to fall onto the floor.
During a test, the robot goes to the ball and picks it up, but then does not move. Which step is faulty?
Ada the beaver has marbles with the following features:
- Size: small, medium or large.
- Color: red, blue or yellow.
- Material: stone, glass or metal.
- Decoration: plain, striped or dotted.
Ada knows that the marble features obey these rules:
- Each marble has exactly one size, one color, one material and one decoration.
- Metal marbles are not large.
- Stone marbles cannot be red or yellow.
- Striped decoration cannot be used for stone or metal marbles.
- Dotted decoration cannot be used for metal marbles.
Ada has a large blue marble. What material is it made of?
Five beavers take toys from a tray. They have the following conversation:
- Beaver A: “To the left of the toy I took is a monkey with the number 1.”
- Beaver E: “My toy is a dog with the number 3.”
- Beaver D: “To the left of the toy I took is the toy E took.”
- Beaver C: “The toy D took is below my toy.”
- Beaver B: “My toy is below A’s toy and to the left of C’s toy.”
Which tray below did the beavers take their toys from?
When Wanda the beaver finds a spider web, she redraws it as follows:
- Number the points where the web is attached to the wall from 1 to $N$.
- Draw an $N × N$ square grid.
- If points $X$ and $Y$ are connected by a thread, shade the cell in row $X$, column $Y$, and the cell in row $Y$, column $X$.
The example below shows a web and its shaded grid.
Xavier the beaver wants to represent letters using 0s and 1s. He notices that T and E occur most often, so he uses fewer 0s and 1s for them, as shown in the table.
| Letter | T | E | A | K | C | R |
| --- | --- | --- | --- | --- | --- | --- |
| Code | 1 | 00 | 0010 | 0110 | 1010 | 1110 |
Lucie the beaver encodes each letter using the alphabet grid below.
| Column 1 | Column 2 | Column 3 | Column 4 | Column 5 |
| --- | --- | --- | --- | --- |
| A | B | C | D | E |
| F | G | H | I | J |
| K | L | M | N | O |
| P | R | S | T | U |
| V | W | X | Y | Z |
After encoding, she can write her brother’s name PAVEL as follows:
Julia enjoys making products from available materials and can sell them for money. The table gives their selling prices and the materials needed to make them.
If Julia has 4 tires, 4 bags of iron and 1 box of wood, what is the greatest total value of products she can recycle?
**Approved unit clarification:** The original wording “4 bags of iron and 1 box of wood” is retained above. For the source’s intended interpretation, use 4 iron tubes and 1 wooden bar, together with 4 tires. The source gives no number of tubes per bag or bars per box.
Alex and Julia play a leaf-taking game with three plates containing 1, 2 and 3 leaves respectively. On each turn, a player may take any positive number of leaves, but only from one plate. The winner is the player who takes the last leaf or leaves from the plates.
Alex plays first. From which plate should he take leaves on his first turn to guarantee victory even if Julia plays as well as possible?
