2024 Advent Calendar - Math Kangaroo USA

One Math Kangaroo Question a day makes you smarter they say! Our German Kangaroo friends have shared this delightful Math Advent Calendar—a collection of pre-Christmas puzzles in Kangaroo style.

2024 Math Kangaroo Advent Calendar Maxi

✨ The Maxi Calendar presents more challenging Christmas puzzles for children in Grades 4 to 6.

/24

Grades 4-6

Days 1-24

Let the countdown to Christmas be both festive and educational! 🎄🦘

1 / 24

Category: 2024 Math Kangaroo Advent Calendar Maxi

1.
Eleonora walks with her parents and her friend Coco in the snowy wildlife park. They are curious to see what the animals do in winter.
They start at the Thick lime, pass the wild boars and cross the bridge on the direct way to the waterfall. There everyone marvels at the huge icicles. After
the waterfall they turn right. At the barn with the hay bales for the winter, they turn right again. At the forester’s lodge they take a break and look at the map.
“In all the animal enclosures we passed, we saw exactly 3 animals,” Eleonora notes. “Except for the donkeys,” says Coco, “they were all hiding.”
How many animals could we see on the way to the forester’s lodge?

12

14

15

17

21

That’s not quite correct. 🤔
We followed the path outlined in the text from Thick lime to the forester's lodge, counting the animal enclosures along the way.
In total, there are six enclosures: wild boar, donkeys, ferrets, deer, geese, and roe deer.
However, the donkeys were hidden, so we only observed animals in five of the enclosures.
Since there were exactly three animals visible in each enclosure, we saw a total of 5 x 3 = 15 animals along the path.

Yes, your answer is correct! 🎉
We followed the path outlined in the text from Thick lime to the forester's lodge, counting the animal enclosures along the way.
In total, there are six enclosures: wild boar, donkeys, ferrets, deer, geese, and roe deer.
However, the donkeys were hidden, so we only observed animals in five of the enclosures.
Since there were exactly three animals visible in each enclosure, we saw a total of 5 x 3 = 15 animals along the path.

2 / 24

Category: 2024 Math Kangaroo Advent Calendar Maxi

2.
Marlene discovered ladybirds in a crack in the wall. Some had 2 points and the others had 7 points.
“The ladybirds were sitting close together, it looked like they were cuddling,” says Marlene. “This is how they protect themselves from the cold,” Marlene’s
mother explains. Marlene’s little brother Matteo wants to know how many points the ladybirds had in total.
“I didn’t count,” says Marlene. “But I remember that there were as many 2-point ladybirds as 7-point ladybirds.”
How many points could there have been in TOTAL?

12

23

34

45

56

That’s not quite correct. 🤔

Since Marlene remembers there were as many 2-point ladybirds as 7-point ladybirds, let's assume there are ladybirds of each type.
The total points from the 2-point ladybirds is .
The total points from the 7-point ladybirds is .
Adding these together:
So, the total number of points is 9 times the number of ladybird pairs.
For example:
If there is 1 pair (1 of each type), the total is points.
If there are 2 pairs, the total is points.
If there are 3 pairs, the total is points.
Answer: The total points depend on the number of pairs, and they are always a multiple of 9 (e.g., 9, 18, 27, 36, 45 etc.).

Yes, your answer is correct! 🎉

Since Marlene remembers there were as many 2-point ladybirds as 7-point ladybirds, let's assume there are x ladybirds of each type.
The total points from the 2-point ladybirds is 2x.
The total points from the 7-point ladybirds is 7x.
Adding these together:
2x+7x=9x
So, the total number of points is 9 times the number of ladybird pairs.
For example:
If there is 1 pair (1 of each type), the total is 9 points.
If there are 2 pairs, the total is 18 points.
If there are 3 pairs, the total is 27 points.
Answer: The total points depend on the number of pairs, and they are always a multiple of 9 (e.g., 9, 18, 27, 36, 45 etc.).

3 / 24

Category: 2024 Math Kangaroo Advent Calendar Maxi

3.
Sebastian goes for a walk with his 5 young dachshunds. All of them are wearing a thick jumper to keep them nice and warm.
Jack’s jumper is not plain.
Einstein’s jumper even has more than 2 colours.
Daisy’s jumper is striped.
Maggie’s jumper has ducks on it.
Kalle’s jumper is plain orange.
Which of these dachshunds is Jack?

U

K

D

E

N

That’s not quite correct. 🤔
The only striped sweater is at position (U), belonging to Daisy. The single-colored sweater, an orange one, is at position (E) and worn by Kalle. The only remaining sweater with more than two colors is at position (K), belonging to Einstein. The sweater with ducks, at position (N), is worn by Maggie. Therefore, Jack is the dachshund at position (D).

Yes, your answer is correct! 🎉
The only striped sweater is at position (U), belonging to Daisy. The single-colored sweater, an orange one, is at position (E) and worn by Kalle. The only remaining sweater with more than two colors is at position (K), belonging to Einstein. The sweater with ducks, at position (N), is worn by Maggie. Therefore, Jack is the dachshund at position (D).

4 / 24

Category: 2024 Math Kangaroo Advent Calendar Maxi

4.
After playing outside, Hannah and Jonas drink a cup of warm tea in the kitchen.
On the kitchen table they discover a puzzle in a magazine:

The names of animals are to be searched for. Letter by letter may be read so that the next letter is always directly above, below, to the left of or to the right of it. Jonas immediately discovers the word LACHS: He starts at the bottom left at the L and goes from there first to the right, then up, up again and then to the left.
Which of the following animals CANNOT be found like this?

SCHAF

OCHSE

DACHS

FROSCH

FISCH

That’s not quite correct. 🤔
Here you can see where SCHAF, OCHSE, DACHS, and FISCH are hiding:
The FROSCH cannot be located in the specified manner.

Yes, your answer is correct! 🎉
Here you can see where SCHAF, OCHSE, DACHS, and FISCH are hiding:
The FROSCH cannot be located in the specified manner.

5 / 24

Category: 2024 Math Kangaroo Advent Calendar Maxi

5.
While playing in the forest, we saw a pile of building material. A second fence was built around the rectangular wild boar enclosure. This is to better protect the wild boars from swine fever. The old fence is 150 meters long and 100 meters wide. The new fence is exactly 2 meters from the old fence on all four sides.

How many meters longer is the new fence than the old one?

12 meters

16 meters

20 meters

22 meters

30 meters

That’s not quite correct. 🤔
The approach of dividing the new fence into parts to directly calculate the difference in length is a great way to simplify the problem.
Here's how that works:
Explanation:
The extra length comes from the 2 m extension on each of the 8 sections (4 sides, each split into two ends).
For each section, the added length is 2m, and there are 8 sections in total.
Thus, the additional length is: 8×2=16m

Yes, your answer is correct! 🎉
The approach of dividing the new fence into parts to directly calculate the difference in length is a great way to simplify the problem.
Here's how that works:
Explanation:
The extra length comes from the 2 m extension on each of the 8 sections (4 sides, each split into two ends).
For each section, the added length is 2m, and there are 8 sections in total.
Thus, the additional length is: 8×2=16m

6 / 24

Category: 2024 Math Kangaroo Advent Calendar Maxi

6.
Today, on St Nicholas’ Day, the siblings Lisa, Tim, Ella and Pia scurried to their boots as soon as they got up. Between oranges, apples and nuts, a chocolate
animal was hidden in each boot. When Aunt Birgit comes in the afternoon, the children ask her a riddle:
“In our boots were a kangaroo, a beaver, a frog and a hedgehog made of chocolate. You have to guess who got which animal.”
The children give three clues:
“Lisa got a beaver.”
“Tim didn’t get a frog.”
“Ella didn’t get a kangaroo.”
Aunt Birgit thinks and realizes: “I can’t solve the riddle like that. There are several possibilities.”
The children think of a fourth clue. Now Aunt Birgit can really find out who got which animal.
What could the fourth clue be?

X: “Tim got a kangaroo.”

W: “Pia didn’t get a beaver.”

O: “Ella got a frog.”

B: “Tim didn’t get a hedgehog.”

Y: “Pia got a frog.”

That’s not quite correct. 🤔
With the first three clues, three possibilities remain regarding which chocolate animal each person has in the boot:
- With clue (X), possibilities 1 and 2 remain.
- The aunt cannot clearly determine who found which chocolate animal.
- With clue (W), possibilities 1, 2, and 3 remain.
- With clue (O), possibilities 1 and 3 remain.
- With clue (B), possibilities 1 and 2 remain.
Even with these clues, the aunt still cannot clearly identify who received which animal. However, with clue (Y), only one possibility remains, specifically possibility 2. Therefore, clue (Y) is the one we are looking for.

Yes, your answer is correct! 🎉
With the first three clues, three possibilities remain regarding which chocolate animal each person has in the boot:
- With clue (X), possibilities 1 and 2 remain.
- The aunt cannot clearly determine who found which chocolate animal.
- With clue (W), possibilities 1, 2, and 3 remain.
- With clue (O), possibilities 1 and 3 remain.
- With clue (B), possibilities 1 and 2 remain.
Even with these clues, the aunt still cannot clearly identify who received which animal. However, with clue (Y), only one possibility remains, specifically possibility 2. Therefore, clue (Y) is the one we are looking for.

7 / 24

Category: 2024 Math Kangaroo Advent Calendar Maxi

7.
At our school we are choosing a school mascot this week. There are 5 animals to choose from. All children are allowed to cast one vote.
In the secretary’s office there is a list of the votes that have been counted so far:
There are still 12 votes missing from class 4b.
The animal with the most votes at the end will be the school mascot. Which animal could that be?

only the stork or the fox

only the beaver

only the hedgehog or the beaver

only the raven

only the stork, the hedgehog or the beaver

That’s not quite correct. 🤔
According to the votes counted so far, the Beaver is currently in the lead. If all 12 children from class 4b vote for the Beaver, it will still remain ahead and win the election. Therefore, the Beaver's victory is possible.
The Hedgehog has the second most votes, standing at 22. If all 12 children from class 4b vote for the Hedgehog, he would then have a total of 22 + 12 = 34 votes. This would allow the Hedgehog to overtake the Beaver, who would then have only 31 votes. Thus, the Hedgehog could potentially win the election.
The Stork is in third place, with 16 votes so far. Even if all 12 remaining votes go to the Stork, he would only reach 16 + 12 = 28 votes, which is still fewer than the Beaver's total. Therefore, the Stork cannot win the election.
It is also clear that the two animals with fewer votes than the Stork cannot win.
Consequently, only the Hedgehog or the Beaver can become the school mascot.

Yes, your answer is correct! 🎉
According to the votes counted so far, the Beaver is currently in the lead. If all 12 children from class 4b vote for the Beaver, it will still remain ahead and win the election. Therefore, the Beaver's victory is possible.
The Hedgehog has the second most votes, standing at 22. If all 12 children from class 4b vote for the Hedgehog, he would then have a total of 22 + 12 = 34 votes. This would allow the Hedgehog to overtake the Beaver, who would then have only 31 votes. Thus, the Hedgehog could potentially win the election.
The Stork is in third place, with 16 votes so far. Even if all 12 remaining votes go to the Stork, he would only reach 16 + 12 = 28 votes, which is still fewer than the Beaver's total. Therefore, the Stork cannot win the election.
It is also clear that the two animals with fewer votes than the Stork cannot win.
Consequently, only the Hedgehog or the Beaver can become the school mascot.

8 / 24

Category: 2024 Math Kangaroo Advent Calendar Maxi

8.
Jule, Milan, Lara, Paul and Zo´e baked biscuits at Paul’s house. They found great animal biscuit cutters and baked kangaroos, hedgehogs and rabbits.
After baking, they realize:
One hedgehog weighs just as much as one rabbit.
One kangaroo weighs as much as two rabbits.
And now it’s time to taste! Everyone takes a plate of biscuits.
Jule has the most biscuits on her plate.
Milan has fewer biscuits on his plate than Jule, but they weigh the same as the biscuits on Jules’ plate.
Which plate is Milan’s?

P

D

A

S

N

That’s not quite correct. 🤔
We count the cookies on the plates and observe that plate (S) has the most cookies—6 cookies. Thus, plate (S) belongs to Jule. The cookies on Jule's plate weigh as much as 6 rabbits.
Next, we analyze the weights of the cookies on the other plates:
Plate (P): Weighs as much as 6 rabbits.
Plate (D): Weighs as much as 5 rabbits.
Plate (A): Weighs as much as 7 rabbits.
Plate (N): Weighs as much as 5 rabbits.
Since Milan's plate must weigh the same as Jule's plate (6 rabbits) but have fewer cookies, plate (P) is Milan's plate.
Conclusion: Milan's plate is plate (P).

Yes, your answer is correct! 🎉
We count the cookies on the plates and observe that plate (S) has the most cookies—6 cookies. Thus, plate (S) belongs to Jule. The cookies on Jule's plate weigh as much as 6 rabbits.
Next, we analyze the weights of the cookies on the other plates:
Plate (P): Weighs as much as 6 rabbits.
Plate (D): Weighs as much as 5 rabbits.
Plate (A): Weighs as much as 7 rabbits.
Plate (N): Weighs as much as 5 rabbits.
Since Milan's plate must weigh the same as Jule's plate (6 rabbits) but have fewer cookies, plate (P) is Milan's plate.
Conclusion: Milan's plate is plate (P).

9 / 24

Category: 2024 Math Kangaroo Advent Calendar Maxi

9.
The dog robot Robbie is demonstrated in the Museum of Technology. He is steered through the course using a remote control with 4 buttons:
The museum guide explains: “Robbie doesn’t run into the obstacles. If you steer him towards an obstacle, he simply stops.”
Which of the sequences of buttons below will take Robbie to the bone?

G

B

A

J

Z

That’s not quite correct. 🤔
We illustrate Robbie's paths using a pen or by tracing them with a finger. Robbie can only reach the bone by pressing the (J) key.
First, Robbie moves forward 2 spaces and then turns to the right. Next, he runs backward 4 spaces between the walls. After that, he turns to the left, runs forward 2 spaces, and finally lands on the bone.

Yes, your answer is correct! 🎉
We illustrate Robbie's paths using a pen or by tracing them with a finger. Robbie can only reach the bone by pressing the (J) key.
First, Robbie moves forward 2 spaces and then turns to the right. Next, he runs backward 4 spaces between the walls. After that, he turns to the left, runs forward 2 spaces, and finally lands on the bone.

10 / 24

Category: 2024 Math Kangaroo Advent Calendar Maxi

10.
Lina learns at the nature conservation center that bearded vultures have some feathers bleached before they are released into the wild. This makes it possible to recognize them later when observing them in flight. This year 5 bearded vultures were released.
Bavaria had more feathers bleached than Recka but less than Dagmar.
Wally and Herculis have no bleached feathers on their tails.
Which of the following pictures shows Bavaria?

M

T

N

R

S

That’s not quite correct. 🤔
We first count the number of bleached feathers in each of the bearded vultures: (M) has 5, (T) has 6, (N) has 5, (R) has 5, and (S) has 4.
It is established that more feathers were bleached in Bavaria than in Recka, but fewer than in Dagmar. Therefore, we conclude that Dagmar must have 6 bleached feathers, Bavaria has 5, and Recka has 4. This indicates that Dagmar is represented by (T) and Recka by (S).
Among the remaining three bearded vultures, only those at (M) and (N) do not have bleached tail feathers, which means they are Wally and Herculis.
Additionally, the bearded vulture at (R) is identified as Bavaria.

Yes, your answer is correct! 🎉

We first count the number of bleached feathers in each of the bearded vultures: (M) has 5, (T) has 6, (N) has 5, (R) has 5, and (S) has 4.
It is established that more feathers were bleached in Bavaria than in Recka, but fewer than in Dagmar. Therefore, we conclude that Dagmar must have 6 bleached feathers, Bavaria has 5, and Recka has 4. This indicates that Dagmar is represented by (T) and Recka by (S).
Among the remaining three bearded vultures, only those at (M) and (N) do not have bleached tail feathers, which means they are Wally and Herculis.
Additionally, the bearded vulture at (R) is identified as Bavaria.

11 / 24

Category: 2024 Math Kangaroo Advent Calendar Maxi

11.
Antonia and Liam visit Liam’s aunt, who is a beekeeper. This year her bees have produced a lot of honey.
Antonia and Liam look at a fragment of a honeycomb:
“The honeycombs are hexagonal,” says Antonia. “And all of them are quite regular,” adds Liam. A piece is missing from the middle of the fragment.
Which piece fits into the gap?

X

B

Y

H

Q

That’s not quite correct. 🤔
We fill in the edges of the missing honeycombs.
Now, the gap can be easily compared with the possible answers. The piece (Q) fits into the gap.

Yes, your answer is correct! 🎉
We fill in the edges of the missing honeycombs.
Now, the gap can be easily compared with the possible answers. The piece (Q) fits into the gap.

12 / 24

Category: 2024 Math Kangaroo Advent Calendar Maxi

12.
Frieda has discovered snails in a sheltered spot in the garden. “The snails hibernate there,” her mother explained to her. She learned how to draw snails
from a book: Frieda draws quarter circles on squares with a compass. She starts with a small square that is 1 box wide. Then she places more squares counterclockwise that fit: another square that is 1 box wide, then a square that is 2 boxes wide, and so on.
Two paper squares have accidentally fallen down.
Which two squares complete the snail spiral?

E

U

N

L

B

That’s not quite correct. 🤔
For this task, both the direction of the circle's arcs and the sizes of the paper squares must be considered.
Counting the missing squares in the snail, we find that their side lengths must be 3 boxes and 8 boxes wide. Only answer option (B) meets these requirements, as all other options include at least one square with an incorrect side length.
Additionally, the direction of the circular arcs in (B) matches perfectly. Thus, these squares complete the snail spiral accurately.
Theoretically, the paper squares could also be rotated. However, only the squares in (B) have the correct dimensions, making the solution uniquely determined.
The side lengths of the squares in the spiral follow the Fibonacci sequence, where each number is the sum of the two preceding ones. This characteristic further confirms the accuracy of the solution.

Yes, your answer is correct! 🎉
For this task, both the direction of the circle's arcs and the sizes of the paper squares must be considered.
Counting the missing squares in the snail, we find that their side lengths must be 3 boxes and 8 boxes wide. Only answer option (B) meets these requirements, as all other options include at least one square with an incorrect side length.
Additionally, the direction of the circular arcs in (B) matches perfectly. Thus, these squares complete the snail spiral accurately.
Theoretically, the paper squares could also be rotated. However, only the squares in (B) have the correct dimensions, making the solution uniquely determined.
The side lengths of the squares in the spiral follow the Fibonacci sequence, where each number is the sum of the two preceding ones. This characteristic further confirms the accuracy of the solution.

13 / 24

Category: 2024 Math Kangaroo Advent Calendar Maxi

13.
Pina is supposed to go buy cat food after school. Her cat Bella likes the Casimir brand best. The Christmas varieties are on sale right now.
Pina is supposed to buy exactly 12 cans and spend as little money as possible on them. She thinks about how she can combine the offers.
What is the lowest price Pina has to pay for 12 cans?

10.00 euros

10.20 euros

10.50 euros

10.70 euros

10.80 euros

That’s not quite correct. 🤔
Try combinations of packs to get 12 cans
Case 1: Use two 5-packs and two single cans
Two 5-packs =
Two single cans =
Total = €8.20 + €2.00 = €10.20
Case 2: Use one 8-pack and one 4-pack
One 8-pack = €6.80
One 4-pack = €3.60
Total = €6.80 + €3.60 = €10.40
Case 3: Use one one 5-pack, one 4-pack and three single can
One 5-pack = €4.10
One 4-pack = €3.60
Three single can = €3.00
Total = €4.10 + €3.60 + €3.00 = €10.70
Case 4: Use three 4-packs
Three 4-packs =
Total = €10.80
Step 3: Choose the lowest cost
The lowest cost is achieved in Case 1, where Pina buys two 5-packs and two single cans for a total of €10.20.
Final Answer: €10.20

Yes, your answer is correct! 🎉
Try combinations of packs to get 12 cans
Case 1: Use two 5-packs and two single cans
Two 5-packs =
Two single cans =
Total = €8.20 + €2.00 = €10.20
Case 2: Use one 8-pack and one 4-pack
One 8-pack = €6.80
One 4-pack = €3.60
Total = €6.80 + €3.60 = €10.40
Case 3: Use one one 5-pack, one 4-pack and three single can
One 5-pack = €4.10
One 4-pack = €3.60
Three single can = €3.00
Total = €4.10 + €3.60 + €3.00 = €10.70
Case 4: Use three 4-packs
Three 4-packs =
Total = €10.80
Step 3: Choose the lowest cost
The lowest cost is achieved in Case 1, where Pina buys two 5-packs and two single cans for a total of €10.20.
Final Answer: €10.20

14 / 24

Category: 2024 Math Kangaroo Advent Calendar Maxi

14.
In the cage of our two budgies, Amadeus and Krümel, I placed a large mirror diagonally in one corner.
If Amadeus looks in the mirror as in the picture, he sees Krümel and the food bowl. What could Amadeus see in the mirror?

W

V

F

P

O

That’s not quite correct. 🤔
When Amadeus looks into the mirror, turning to the left shows items positioned farther forward in the cage, while turning to the right reveals items positioned farther back.
As a result, in the mirror, the food bowl appears to the right of Krümel. This observation is true only for options (V) and (F). Since Krümel is facing the food bowl, the correct mirror image is option (F).

Yes, your answer is correct! 🎉
When Amadeus looks into the mirror, turning to the left shows items positioned farther forward in the cage, while turning to the right reveals items positioned farther back.
As a result, in the mirror, the food bowl appears to the right of Krümel. This observation is true only for options (V) and (F). Since Krümel is facing the food bowl, the correct mirror image is option (F).

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Category: 2024 Math Kangaroo Advent Calendar Maxi

15.
The mild weather has made the mole pair Gregor and Mila lively. They quickly created 4 molehills on the meadow. They look at their work in the sunset.
Gregor looks out of one of the 4 molehills and Mila out of another.
How many different possibilities are there for this?

8

10

12

16

18

That’s not quite correct. 🤔
To solve this, we calculate how many ways Gregor and Mila can each occupy a molehill. There are 4 molehills, and both Gregor and Mila must choose different ones.
Step 1: Gregor chooses a molehill.
He has 4 choices (any of the 4 molehills).
Step 2: Mila chooses a molehill.
Mila cannot choose the same molehill as Gregor, so she has 3 choices (the remaining molehills).
Step 3: Multiply the choices.
The total number of possibilities is
Final Answer: 12

Yes, your answer is correct! 🎉
To solve this, we calculate how many ways Gregor and Mila can each occupy a molehill. There are 4 molehills, and both Gregor and Mila must choose different ones.
Step 1: Gregor chooses a molehill.
He has 4 choices (any of the 4 molehills).
Step 2: Mila chooses a molehill.
Mila cannot choose the same molehill as Gregor, so she has 3 choices (the remaining molehills).
Step 3: Multiply the choices.
The total number of possibilities is
Final Answer: 12

16 / 24

Category: 2024 Math Kangaroo Advent Calendar Maxi

16.
Tilman has built a race track with his uncle for his two mice Ping and Pong.
It consists of a square and a pentagon. The sides of the pentagon are the same length as the sides of the square.
Right at the first test, the two mice run off in different directions from the starting point. They are both equally fast. Ping always runs clockwise around
the square. Pong always runs clockwise around the pentagon.
Tilman has determined with the stopwatch: Pong completes a full lap around the pentagon in exactly 10 seconds.
How many seconds after the start will the mice Ping and Pong meet the next time?

17 seconds

22 seconds

25 seconds

26 seconds

30 seconds

That’s not quite correct. 🤔
Since Pong completes a full lap around the square in 10 seconds, he takes 2 seconds to run along one side. Since all sides of the square track are of equal length, Ping also takes 2 seconds to complete one side.
We observe both mice simultaneously as they run. To make this easier, we label the corners of the track:
We monitor their meetings regularly. In the table, we have recorded the positions of Ping and Pong at the start and then after 2 seconds, after 4 seconds, after 6 seconds, and so on.
They meet again at point D after a duration of 22 seconds.

Yes, your answer is correct! 🎉
Since Pong completes a full lap around the square in 10 seconds, he takes 2 seconds to run along one side. Since all sides of the square track are of equal length, Ping also takes 2 seconds to complete one side.
We observe both mice simultaneously as they run. To make this easier, we label the corners of the track:
We monitor their meetings regularly. In the table, we have recorded the positions of Ping and Pong at the start and then after 2 seconds, after 4 seconds, after 6 seconds, and so on.
They meet again at point D after a duration of 22 seconds.

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Category: 2024 Math Kangaroo Advent Calendar Maxi

17.
Carla and Diego go on an excursion to the children’s farm at the weekend.
They learn from the farmer that the chickens are particularly diligent at the moment. “Yesterday they laid 10 brown and 14 white eggs,” the farmer tells
them. Today Carla and Diego are allowed to collect the freshly laid eggs. They count how many eggs there are of each kind and give the farmer a task: “There are half as many brown eggs today as yesterday, but twice as many white eggs as yesterday.”
The farmer has to find out how many eggs there are in total today.
How many eggs did the hens lay in total today?

25

29

30

33

35

That’s not quite correct. 🤔
We are given:
Yesterday: 10 brown eggs and 14 white eggs.
Today: Half as many brown eggs as yesterday and twice as many white eggs as yesterday.
Step 1: Calculate the number of brown eggs today
Yesterday's brown eggs = 10
Today, there are half as many:
Step 2: Calculate the number of white eggs today
Yesterday's white eggs = 14
Today, there are twice as many:
Step 3: Find the total number of eggs today
Final Answer:
The hens laid 33 eggs in total today.

Yes, your answer is correct! 🎉
We are given:
Yesterday: 10 brown eggs and 14 white eggs.
Today: Half as many brown eggs as yesterday and twice as many white eggs as yesterday.
Step 1: Calculate the number of brown eggs today
Yesterday's brown eggs = 10
Today, there are half as many:
Step 2: Calculate the number of white eggs today
Yesterday's white eggs = 14
Today, there are twice as many:
Step 3: Find the total number of eggs today
Final Answer:
The hens laid 33 eggs in total today.

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Category: 2024 Math Kangaroo Advent Calendar Maxi

18.
There are 5 zebras in our zoo.
The zebras Calipso and Chantal are twins and look exactly the same.
The zebras Rube and Rabauke are also twins and look exactly the same.
The fifth zebra is called Diana, her stripe pattern looks a bit different.
Which zebra is Diana?

O

J

E

L

Q

That’s not quite correct. 🤔
The two zebras located at (J) and (Q) each have an extra stripe around their eye, and their bellies appear slightly different from those of the other three zebras. This indicates that they are a pair of twins. The zebras at (O) and (L) have unique stripe patterns on their hindquarters compared to the other three zebras, identifying them as the second pair of twins. Therefore, the zebra at (E) must be named Diana.

Yes, your solution is correct! 🎉
The two zebras located at (J) and (Q) each have an extra stripe around their eye, and their bellies appear slightly different from those of the other three zebras. This indicates that they are a pair of twins. The zebras at (O) and (L) have unique stripe patterns on their hindquarters compared to the other three zebras, identifying them as the second pair of twins. Therefore, the zebra at (E) must be named Diana.

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Category: 2024 Math Kangaroo Advent Calendar Maxi

19.
Anna, Nele, Alina, Linus and Ella are playing in the snow. Four of them draw letters in the snow, each of them all the letters of their own name.
The fifth child has taken the neighbor's cat in its arms and therefore cannot draw any letters in the snow.
Which child has the cat in its arms?

ANNA

NELE

ALINA

LINUS

ELLA

That’s not quite correct. 🤔
We count how often the letters appear in the names and in the snow.
From the count, one A, one E, and two L's are missing. These letters spell out the name "ELLA." Therefore, Ella is the one holding the cat in her arms! 🐾

Yes, your solution is correct! 🎉
We count how often the letters appear in the names and in the snow.
From the count, one A, one E, and two L's are missing. These letters spell out the name "ELLA." Therefore, Ella is the one holding the cat in her arms! 🐾

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Category: 2024 Math Kangaroo Advent Calendar Maxi

20.
Meike and Gregor are in the zoo. They want to watch the feeding of the penguins. Just before it starts, five penguins are already standing neatly in a
row, waiting quietly. Meike and Gregor take a photo of them. Meike took this photo from the left:
Gregor took a photo from the right at the same time.
What does Gregor’s photo look like?

A

Z

P

G

C

That’s not quite correct. 🤔
Since all the cords in the photo from the left are pointing to the left, in the photo from the right, all the cords must point to the right. Therefore, photos (Z) and (P) are eliminated.
The smallest penguin, visible on the far left in the photo from the left, must appear on the far right in the photo from the right. This means the correct photo can only be photo (C).
Photo (C) is the mirrored version of the photo from the left. To confirm this, you can hold the sheet against the light, look at the photo from the left from behind, and compare this view with the possible solutions.
Thus, the solution is photo (C).

Yes, your solution is correct! 🎉
Since all the cords in the photo from the left are pointing to the left, in the photo from the right, all the cords must point to the right. Therefore, photos (Z) and (P) are eliminated.
The smallest penguin, visible on the far left in the photo from the left, must appear on the far right in the photo from the right. This means the correct photo can only be photo (C).
Photo (C) is the mirrored version of the photo from the left. To confirm this, you can hold the sheet against the light, look at the photo from the left from behind, and compare this view with the possible solutions.
Thus, the solution is photo (C).

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Category: 2024 Math Kangaroo Advent Calendar Maxi

21.
A medieval Christmas market has opened nearby. There are 24 booths of craftswomen and craftsmen there. They are numbered from 1 to 24.
A spider web is attached to each 1 as decoration. All other numbers are clear.
How many spider webs in total are there on the numbers of the 24 booths?

10

13

15

17

20

That’s not quite correct. 🤔
The digit 1 appears in:
The ones place in the numbers 1, 11, and 21 (3 occurrences).
The tens place in the 10 numbers from 10 to 19.
Thus, the total count is 3 + 10 = 13.
Therefore, there are 13 spider webs where the digit 1 appears.

Yes, your solution is correct! 🎉
The digit 1 appears in:
The ones place in the numbers 1, 11, and 21 (3 occurrences).
The tens place in the 10 numbers from 10 to 19.
Thus, the total count is 3 + 10 = 13.
Therefore, there are 13 spider webs where the digit 1 appears.

22 / 24

Category: 2024 Math Kangaroo Advent Calendar Maxi

22.
The ice floe on which Waldemar the walrus usually takes his nap has broken into several pieces:
4 triangles, 2 squares of different sizes and one pentagon.
Waldemar pushes all the pieces back together. During the night, hopefully they will freeze together again.
What might Waldemar’s ice floe look like?

S

Y

W

U

H

That’s not quite correct. 🤔
In (S), there is a hexagon in place of the base.
In (Y), there are two rectangles but no squares, and there are only 3 triangles instead of 4.
In (W), the squares are the same size, and instead of a polygon, there is a quadrilateral, specifically a trapezoid.
In (H), a rhombus replaces a square.
Only ice floe (U) matches the criteria: 4 triangles, 2 squares of different sizes, and a polygon.
Thus, (U) is the correct answer.

Yes, your solution is correct! 🎉
In (S), there is a hexagon in place of the base.
In (Y), there are two rectangles but no squares, and there are only 3 triangles instead of 4.
In (W), the squares are the same size, and instead of a polygon, there is a quadrilateral, specifically a trapezoid.
In (H), a rhombus replaces a square.
Only ice floe (U) matches the criteria: 4 triangles, 2 squares of different sizes, and a polygon.
Thus, (U) is the correct answer.

23 / 24

Category: 2024 Math Kangaroo Advent Calendar Maxi

23.
Sabrina and Timo visit a reindeer enclosure. The reindeer is the only species of deer in which both the male and female animals have antlers. Every year
they shed them and grow new ones.
There are 3 curious reindeer standing by the fence. “The antlers have many ends – these are the tips on the antlers,” Timo knows. The two look closely
at the antlers.
The first reindeer peers over the fence, it has the biggest antlers:
His antlers have as many ends as the antlers of the second reindeer and the antlers of the third reindeer together.
The second reindeer’s antlers have 4 more ends than the third reindeer’s antlers.
How many ends does the third reindeer’s antlers have?

5

6

7

8

9

That’s not quite correct. 🤔
Let's walk through the steps to solve this problem.
The third reindeer's antlers: We need to figure out how many ends the third reindeer has.
The second reindeer's antlers: It has 4 more ends than the third reindeer.
The first reindeer's antlers: The total number of ends on the first reindeer's antlers is the sum of the ends on the second and third reindeer.
We are given that the first reindeer has 18 ends. Now, let's work through the possibilities.
Table of possible values:
3rd reindeer 2nd reindeer (3rd + 4) 1st reindeer (2nd + 3rd)
0 4 4
1 5 6
2 6 8
3 7 10
4 8 12
5 9 14
6 10 16
7 11 18
8 12 20
Explanation:
When the third reindeer has 7 ends, the second reindeer will have ends.
The first reindeer will then have ends, which matches the given number.
Therefore, the third reindeer has 7 ends.

Yes, your solution is correct! 🎉
Let's walk through the steps to solve this problem.
The third reindeer's antlers: We need to figure out how many ends the third reindeer has.
The second reindeer's antlers: It has 4 more ends than the third reindeer.
The first reindeer's antlers: The total number of ends on the first reindeer's antlers is the sum of the ends on the second and third reindeer.
We are given that the first reindeer has 18 ends. Now, let's work through the possibilities.
Table of possible values:
3rd reindeer 2nd reindeer (3rd + 4) 1st reindeer (2nd + 3rd)
0 4 4
1 5 6
2 6 8
3 7 10
4 8 12
5 9 14
6 10 16
7 11 18
8 12 20
Explanation:
When the third reindeer has 7 ends, the second reindeer will have ends.
The first reindeer will then have ends, which matches the given number.
Therefore, the third reindeer has 7 ends.

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Category: 2024 Math Kangaroo Advent Calendar Maxi

24.

Happy Holidays ( Fröhliche Ferine)

The hedgehog hibernates (Der IGEL IGEL HÄLT WINTERSCHLAF)

That’s not quite correct. 🤔
We enter the correct solution letters into the solution grid:
The decryption process:
The solution word was encrypted using Matheo's method. To decrypt it, we first write the digits of the date 24.12.2022 above the message repeatedly until every letter has a number assigned above it:
B A Q G E E J F Y H S U G N R C P O B F J A D
2 4 1 2 2 0 2 2 2 4 1 2 2 0 2 2 2 4 1 2 2 0 2
Now, we replace each letter with the letter that is as many positions further in the alphabet as the number written above it indicates. For example:
The B at the beginning is replaced with D, which is 2 positions after B.
The A is replaced with E, which is 4 positions after A.
The Q is replaced with R, which is 1 position after Q.
The first part of the decrypted solution is: DER.
Continuing this process:
G → I
E → G
E → E (unchanged since the number above it is 0)
J → L
...
When fully decrypted, the solution word forms a phrase that describes something a familiar animal does in winter. The final solution is:
DER IGEL HÄLT WINTERSCHLAF
(The hedgehog hibernates).

Yes, your solution is correct! 🎉
We enter the correct solution letters into the solution grid:
The decryption process:
The solution word was encrypted using Matheo's method. To decrypt it, we first write the digits of the date 24.12.2022 above the message repeatedly until every letter has a number assigned above it:
B A Q G E E J F Y H S U G N R C P O B F J A D
2 4 1 2 2 0 2 2 2 4 1 2 2 0 2 2 2 4 1 2 2 0 2
Now, we replace each letter with the letter that is as many positions further in the alphabet as the number written above it indicates. For example:
The B at the beginning is replaced with D, which is 2 positions after B.
The A is replaced with E, which is 4 positions after A.
The Q is replaced with R, which is 1 position after Q.
The first part of the decrypted solution is: DER.
Continuing this process:
G → I
E → G
E → E (unchanged since the number above it is 0)
J → L
...
When fully decrypted, the solution word forms a phrase that describes something a familiar animal does in winter. The final solution is:
DER IGEL HÄLT WINTERSCHLAF
(The hedgehog hibernates).

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