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stringlengths 36
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|---|---|---|---|---|---|
3297f045-50a5-4b81-8823-acfe231b6a50
|
101
|
As shown in <image>,Every night the wizard Tilim makes the weather forecast for the king. When Tilim gets it right he gets 3 gold coins, but when he makes a mistake, he pays a fine of 2 gold coins. After making the prediction for 5 days, Tilim did the math and discovered that he neither won nor lost coins. How many times did he get the weather forecast right in those 5 days?
<image1>
|
MathVision
|
2
| |
d649cc5d-87c5-4a10-a588-f438c7a95d01
|
102
|
As shown in <image>,A magician takes animals out of his hat always in the same order, as shown below.
<image1>
The pattern of the figure is repeated every five animals. What will be the fourteenth animal he will pull out of his hat?
<image2>
|
MathVision
|
A
| |
7f967456-0d5e-4dbf-9be0-0356e0e2b483
|
103
|
As shown in <image>,Ana has the cards shown on the left. She chooses several of them to assemble the tower shown on the right. Which cards did she not use?
<image1>
<image2>
<image3>
|
MathVision
|
C
| |
6fc84830-eebe-49e8-89c7-803dc866fe35
|
104
|
As shown in <image>,Maria made a block using white cubes and colored cubes in equal amounts. How many of the white cubes cannot be seen in the picture?
<image1>
|
MathVision
|
2
| |
ba744e9e-6ac3-4aa5-9d38-c2141dea1110
|
105
|
As shown in <image>,Ana draws some shapes on a sheet. Her drawing has fewer squares than triangles. What could be her drawing?
<image1>
|
MathVision
|
D
| |
72737e96-67ec-4063-8470-6a09c4e09ec0
|
106
|
As shown in <image>,Which of the tiles below is NOT part of the wall next door?
<image1>
<image2>
|
MathVision
|
E
| |
31b74577-35ab-4893-8bab-c59413b8a698
|
107
|
As shown in <image>,A village of 12 houses has four straight streets and four circular streets. The map shows 11 houses. In each straight street there are three houses and in each circular street there are also three houses. Where should the 12th house be placed on this map?
<image1>
|
MathVision
|
D
| |
7569113e-a466-4e2a-ae01-7aaa2d5fe11f
|
108
|
As shown in <image>,Five blocks are built with equal cubes glued face to face. In which of them was the smallest number of cubes used?
<image1>
|
MathVision
|
A
| |
8c518572-c884-40e9-8aef-21a76553fefe
|
109
|
As shown in <image>,Numbers were written on the petals of two flowers, with a number on each petal. One of the petals is hidden. The sum of the numbers written on the back flower is twice the sum of the numbers written on the front flower. What is the number written on the hidden petal?
<image1>
|
MathVision
|
30
| |
6ed20596-789a-4f6a-ace2-18bec09cb6be
|
110
|
As shown in <image>,Six figures were drawn, one on each side of a cube, as shown beside, in different positions. On the side that does not appear beside is this drawing:
<image1>
What is the figure on the face opposite to it?
<image2>
<image3>
|
MathVision
|
B
| |
24ec4e9c-f2a0-4ce5-9100-f9b6916578a4
|
111
|
As shown in <image>,Maria wants to write whole numbers in the squares of the figure, so that the sum of the numbers in three consecutive squares is always 10. She has already written a number. What number should she write on the gray square?
<image1>
|
MathVision
|
2
| |
e56418ad-12c9-44bd-b691-4c51ca26f789
|
112
|
As shown in <image>,Turning a card around on the top side, we see the photo of the kangaroo. Instead, if we turn the card around on the right side, what will appear?
<image1>
<image2>
|
MathVision
|
D
| |
b5b9ca97-d74f-4bb1-ad9d-45b009b2c38d
|
113
|
As shown in <image>,Tom has these nine cards:
<image1>
He places these cards on the board next to each other so that each horizontal line and each vertical line has three cards with the three different shapes and the three different amounts of drawings. He has already placed three cards, as shown in the picture. Which card should he place in the colored box?
<image2>
<image3>
|
MathVision
|
E
| |
37bac362-a49f-4196-aa21-bb75dea65b72
|
114
|
As shown in <image>,Two equal trains, each with 31 numbered wagons, travel in opposite directions. When the wagon number 7 of a train is side by side with the wagon number 12 of the other train, which wagon is side by side with the wagon number 11 ?
<image1>
|
MathVision
|
8
| |
ea08fcff-7ebc-4695-8758-eae86c688b19
|
115
|
As shown in <image>,Six different numbers, chosen from integers 1 to 9 , are written on the faces of a cube, one number per face. The sum of the numbers on each pair of opposite faces is always the same. Which of the following numbers could have been written on the opposite side with the number 8 ?
<image1>
|
MathVision
|
3
| |
178f10f8-7900-40f6-8505-c6cfe60bc15a
|
116
|
As shown in <image>,Rita numbered the circles of the figure from 1 to 8 , so that the sum of the three numbers on each of the four sides of the square equals 13 . What is the sum of the four numbers written on the colored circles?
<image1>
|
MathVision
|
16
| |
a24356e5-7ae0-42f2-9078-8f8d285ab98b
|
117
|
As shown in <image>,In the figure, an arrow pointing from one person to another means that the first person is shorter than the second. For example, person $B$ is shorter than person $A$. Which person is the tallest?
<image1>
|
MathVision
|
C
| |
94417020-3100-4145-bfd0-6505b96d50a3
|
118
|
As shown in <image>,Maia the bee can only walk on colorful houses. How many ways can you color exactly three white houses with the same color so that Maia can walk from $A$ to $B$ ?
<image1>
|
MathVision
|
16
| |
d75cf546-5184-43f9-8684-20c83ba658a8
|
119
|
As shown in <image>,A kangaroo laid out 3 sticks like this to make a shape. It is not allowed to break or to bend the sticks. Which shape could the kangaroo make?
<image1>
|
MathVision
|
E
| |
93755173-0e8a-4b2c-af16-7548cdc6c89f
|
120
|
As shown in <image>,The picture shows 2 mushrooms. What is the difference between their heights?
<image1>
|
MathVision
|
5
| |
ad67bd55-5e65-4c79-8f80-fb8828ed415f
|
121
|
As shown in <image>,Which of the paths shown in the pictures is the longest?
<image1>
|
MathVision
|
A
| |
d27a43f8-60fc-42d8-9527-a1320804cd3e
|
122
|
As shown in <image>,Four identical pieces of paper are placed as shown. Michael wants to punch a hole that goes through all four pieces. At which point should Michael punch the hole?
<image1>
|
MathVision
|
D
| |
8789cda7-9025-40d8-ab60-ff698da91849
|
123
|
As shown in <image>,Ella puts on this t-shirt and stands in front of a mirror. Which of these images does she see in the mirror?
<image1>
<image2>
|
MathVision
|
A
| |
6f0b4a97-e24c-4d10-93f4-3a01a35b7b56
|
124
|
As shown in <image>,These children are standing in a line. Some are facing forwards and others are facing backwards. How many children are holding another child's hand with their right hand?
<image1>
|
MathVision
|
6
| |
f70f838e-8a61-4aa0-80f5-ffc8b78288b9
|
125
|
As shown in <image>,In the Kangaroo constellation, all stars have a number greater than 3 and their sum is 20 . Which is the Kangaroo constellation?
<image1>
|
MathVision
|
B
| |
b9b3fab3-b574-435c-a49c-06009d44f25a
|
126
|
As shown in <image>,Edmund cut a ribbon as shown in the picture. How many pieces of the ribbon did he finish with?
<image1>
|
MathVision
|
12
| |
1f10e51b-858c-4acd-8337-f32259b19f29
|
127
|
As shown in <image>,Rose the cat walks along the wall. She starts at point $B$ and follows the direction of the arrows shown in the picture. The cat walks a total of 20 metres. Where does she end up?
<image1>
|
MathVision
|
D
| |
497da905-32d3-4ee6-87a9-193b74f06369
|
128
|
As shown in <image>,Julia has two pots with flowers, as shown. She keeps the flowers exactly where they are. She buys more flowers and puts them in the pots. After that, each pot has the same number of each type of flower. What is the smallest number of flowers she needs to buy?
<image1>
|
MathVision
|
8
| |
e5c8cbaa-a0c2-43d8-ae49-d6f721b9bbf0
|
129
|
As shown in <image>,Tom encodes words using the board shown. For example, the word PIZZA has the code $A 2 A 4 C 1 C 1 B 2$. What word did Tom encode as B3B2C4D2?
<image1>
|
MathVision
|
E
| |
aef05402-1e59-4856-99d4-23460024a777
|
130
|
As shown in <image>,Which figure can be made from the 2 pieces shown on the right?
<image1>
<image2>
|
MathVision
|
A
| |
24e56261-105c-414a-9700-43b63fa87142
|
131
|
As shown in <image>,The picture shows the five houses of five friends and their school. The school is the largest building in the picture. To go to school, Doris and Ali walk past Leo's house. Eva walks past Chole's house. Which is Eva's house?
<image1>
<image2>
|
MathVision
|
B
| |
4ed7d350-7ddb-4834-898b-5a25e8fada38
|
132
|
As shown in <image>,Mara built the square by using 4 of the following 5 shapes. Which shape was not used?
<image1>
<image2>
|
MathVision
|
D
| |
8c218999-5320-4ad9-9f66-b808c41eb3ed
|
133
|
As shown in <image>,Every time the witch has 3 apples she turns them in to 1 banana. Every time she has 3 bananas she turns them in to 1 apple. What will she finish with if she starts with 4 apples and 5 bananas?
<image1>
<image2>
|
MathVision
|
A
| |
18ebff20-8375-4ad4-bf78-c340b76520ae
|
134
|
As shown in <image>,The picture beside shows two cogs, each with a black tooth. Where will the black teeth be after the small cog has made one full turn?
<image1>
<image2>
|
MathVision
|
C
| |
ad510835-2ad6-43fb-b4ce-f30ee025a08d
|
135
|
As shown in <image>,Each participant in a cooking contest baked one tray of cookies like the one shown beside. What is the smallest number of trays of cookies needed to make the following plate?
<image1>
|
MathVision
|
3
| |
361b152b-f5fb-4090-b8f3-a6551f91fbc9
|
136
|
As shown in <image>,Stan has five toys: a ball, a set of blocks, a game, a puzzle and a car. He puts each toy on a different shelf of the bookcase. The ball is higher than the blocks and lower than the car. The game is directly above the ball. On which shelf can the puzzle not be placed?
<image1>
|
MathVision
|
3
| |
b80f2ac1-d855-45e1-842d-48e27299d2dd
|
137
|
As shown in <image>,In which box are the most triangles?
<image1>
|
MathVision
|
B
| |
2ca16062-c48e-4fba-90fc-3c7eabdaac89
|
138
|
As shown in <image>,A sandwich and a juice cost 12 Euros together. A sandwich and two juices cost 14 Euros together. How many Euros does one juice cost?
<image1>
|
MathVision
|
2
| |
74192422-1c35-4aa9-8f20-e82d262e2bd1
|
139
|
As shown in <image>,Anna cuts the picture of a mushroom in two halves.
<image1>
She then arranges the two pieces together to form a new picture. What could this new picture look like?
<image2>
|
MathVision
|
E
| |
d087f01b-fbcb-4beb-a31d-7c8d1e692b1a
|
140
|
As shown in <image>,In the four squares of a row there always have to be exactly two coins. In the four squares below each other there also always have to be exactly two coins.
<image1>
On which square does one more coin have to be placed?
|
MathVision
|
D
| |
39a20a4d-938b-4940-a817-6ce08d1dcbf5
|
141
|
As shown in <image>,A monkey has torn off a piece of Captain Jack's map.
<image1>
What does the piece the monkey has torn off look like?
<image2>
|
MathVision
|
B
| |
404cc81d-c967-4920-8b0d-7e771a27b06b
|
142
|
As shown in <image>,These five animals are made up from different shapes. There is one shape which is only used on one animal. On which animal is this shape used?
<image1>
|
MathVision
|
D
| |
4a4f2c06-5502-4794-9daf-a096b1462349
|
143
|
As shown in <image>,There is an animal asleep in each of the five baskets. The koala and the fox sleep in baskets with the same pattern and the same shape. The kangaroo and the rabbit sleep in baskets with the same pattern.
<image1>
In which basket does the mouse sleep?
|
MathVision
|
E
| |
28aafc8a-33e7-4cab-87a9-0d173a3fdf33
|
144
|
As shown in <image>,The picture shows one object made up of 5 identical building blocks.
<image1>
How many building blocks touch exactly 3 others?
|
MathVision
|
2
| |
0c375839-625d-496c-b2ce-5d07b8125e83
|
145
|
As shown in <image>,The kangaroo wants to visit the koala. On its way it is not allowed to jump through a square with water. Each arrow shows one jump on to a neighbouring field.
<image1>
Which path is the kangaroo allowed to take?
<image2>
|
MathVision
|
C
| |
449482cf-5d9d-4bdb-9c9f-4bbc97615566
|
146
|
As shown in <image>,Carl writes down a five-digit number.
He then places a shape on each of the five digits (see picture).
He places different shapes on different digits.
He places the same shape on the same digits.
Which number did Carl hide?
<image1>
|
MathVision
|
34426
| |
1a784db6-a755-441d-93b7-041e8b594f2f
|
147
|
As shown in <image>,Katrin forms a path around each square. For that she uses stones like this
<image1>
How many such stones does she need for a path around the square with side length 5?
|
MathVision
|
12
| |
8c49cf61-437c-4991-a5ca-fa62fe6da4eb
|
148
|
As shown in <image>,Below you see five pieces of lawn. Which one has the smallest area of grass?
<image1>
|
MathVision
|
A
| |
4dff545e-36a7-41b3-a59b-2b592a51d714
|
149
|
As shown in <image>,The numbers in the five circles around each house add up to 20 . Some numbers are missing.
<image1>
Which number does the question mark stand for?
|
MathVision
|
9
| |
4c7c6c4e-c385-4787-9017-259120ce2414
|
150
|
As shown in <image>,Dino walks from the entrance to the exit. He is only allowed to go through each room once. The rooms have numbers (see diagram). Dino adds up all the numbers of the rooms he walks through.
<image1>
What is the biggest result he can get this way?
|
MathVision
|
34
| |
c76b7095-752a-4596-b781-bd274ec6eb39
|
151
|
As shown in <image>,Out of how many circles is the beaver made of?
<image1>
|
MathVision
|
8
| |
a700d07f-1b84-45c3-8ebf-c84372def048
|
152
|
As shown in <image>,The picture shows 5 cubes from the front. What do they look like from above?
<image1>
<image2>
|
MathVision
|
B
| |
2aaab4bc-8fe6-4f50-81eb-367aa723b1b4
|
153
|
As shown in <image>,Each bowl has 4 balls. Add up the numbers on the balls. In which bowl is the result biggest?
<image1>
|
MathVision
|
A
| |
0ff9f04c-7ac3-4307-b2da-a7ba5944b3d3
|
154
|
As shown in <image>,Mr Beaver re-arranges the parts to build a kangaroo.
<image1>
Which part is missing?
<image2>
|
MathVision
|
A
| |
5916a515-a1ac-4562-9085-7d09ad7abcea
|
155
|
As shown in <image>,Sara says: "My boat has more than one circle. It also has 2 triangles more than squares." Which boat belongs to Sara?
<image1>
|
MathVision
|
E
| |
a113e3e6-29f8-4a84-8f9e-fe5c0c139a01
|
156
|
As shown in <image>,The bee on the right has a few pieces missing. Each piece costs points (Punkte).
<image1>
How many points does Maya need to complete the bee?
|
MathVision
|
13
| |
d60567b7-92bd-4918-ad79-7662b690c713
|
157
|
As shown in <image>,Susi folds a piece of paper in the middle. She stamps 2 holes.
<image1>
What does the piece of paper look like when she unfolds it again?
<image2>
|
MathVision
|
B
| |
c4a439bd-1119-48af-ac44-71e72f0576ea
|
158
|
As shown in <image>,Hansi sticks 12 cubes together to make this figure. He always puts one drop of glue between two cubes. How many drops of glue does he need?
<image1>
|
MathVision
|
11
| |
8127c4d5-d8b0-45c6-b21a-65211cb9504a
|
159
|
As shown in <image>,The two markers with a question mark have the same number.
<image1>
Which number do you have to put instead of the question mark so that the calculation is correct?
|
MathVision
|
3
| |
1009697f-6e02-4e63-afda-4d2daea02d98
|
160
|
As shown in <image>,Max wants to complete the jigsaw shown. He has different pieces.
<image1>
Which pieces does he have to use?
<image2>
|
MathVision
|
A
| |
2fa960f1-5a01-4946-aed6-3bb08de0828d
|
161
|
As shown in <image>,Elvis has 6 triangles with this pattern
<image1>
Which picture can he make with them?
<image2>
|
MathVision
|
A
| |
f5b873d7-1309-4d15-83f0-99e903d49e7c
|
162
|
As shown in <image>,Each of the children Ali, Lea, Josef, Vittorio and Sophie get a birthday cake. The number on top of the cake shows how old the child is. Lea is two years older than Josef, but one year younger than Ali. Vittorio is the youngest. Which cake belongs to Sophie?
<image1>
|
MathVision
|
C
| |
b10e1161-ccc1-4c7b-87ea-ee563fd66fa7
|
163
|
As shown in <image>,Maria has a total of 19 apples in 3 bags. She takes the same amount of apples from each bag. Then there are 3, 4 and 6 apples in the bags.
<image1>
How many apples did Maria take from each bag?
|
MathVision
|
2
| |
c9a10d54-5938-4ae3-9aad-101b0c34798b
|
164
|
As shown in <image>,According to the rule given in the left picture below, we construct a numerical triangle with an integer number greater than 1 in each cell. Which of the numbers given in the answers cannot appear in the shaded cell?
<image1>
|
MathVision
|
A
| |
f8a3297a-0072-4ce2-8b1e-bd7f99d67306
|
165
|
As shown in <image>,Let $A B C$ be a triangle with area 30. Let $D$ be any point in its interior and let $e, f$ and $g$ denote the distances from $D$ to the sides of the triangle. What is the value of the expression $5 e+12 f+13 g$?
<image1>
|
MathVision
|
60
| |
b20dcf4a-ccbe-46e2-a56a-aa16ab98a77e
|
166
|
As shown in <image>,The diagram shows two squares: one has a side with a length of 2 and the other (abut on the first square) has a side with a length of 1. What is the area of the shaded zone?
<image1>
|
MathVision
|
1
| |
e17f3784-a352-4fe2-9108-d60aa3a921c4
|
167
|
As shown in <image>,We first draw an equilateral triangle, then draw the circumcircle of this triangle, then circumscribe a square to this circle. After drawing another circumcircle, we circumscribe a regular pentagon to this circle, and so on. We repeat this construction with new circles and new regular polygons (each with one side more than the preceding one) until we draw a 16 -sided regular polygon. How many disjoint regions are there inside the last polygon?
<image1>
|
MathVision
|
248
| |
84bddc75-d51e-4706-83cd-a0517281b7ac
|
168
|
As shown in <image>,In the picture $A B C D$ is a rectangle with $A B=16, B C=12$. Let $E$ be such a point that $A C \perp C E, C E=15$. If $F$ is the point of intersection of segments $A E$ and $C D$, then the area of the triangle $A C F$ is equal to
<image1>
|
MathVision
|
75
| |
a0671e68-0028-4da6-b4bb-45a946d4dde3
|
169
|
As shown in <image>,In a square of side $s$, where $s$ is an odd integer, the squares of side 1 on the diagonals are colored (like in the picture, where the square is of side 7). How many white squares are there?
<image1>
|
MathVision
|
A
| |
5c48b68a-3900-48d7-b705-c8019b6381ac
|
170
|
As shown in <image>,On the circumference of radius $r$ three points $X, Y$ and $A$ are marked such that $X Y=r, X Y \perp A Y$ (see the figure). How many degrees has the angle $X A Y$?
<image1>
|
MathVision
|
30
| |
ba4061e2-2e22-43cb-ad90-9b6270800975
|
171
|
As shown in <image>,The set of all pairs $(x, y)$ which satisfy conditions $x y \leqslant 0$ and $x^{2}+y^{2}=4$ is on the graph:
<image1>
|
MathVision
|
C
| |
4eefcba5-bd26-423a-8273-034243bcc4d6
|
172
|
As shown in <image>,In the figure the two equilateral triangles $A B C$ and $E C D$ have sides of length 2 and 1 respectively. The area of the quadrilateral $A B C E$ is:
<image1>
|
MathVision
|
E
| |
2b9dd88f-0fe9-4018-8b69-03bc1c81f428
|
173
|
As shown in <image>,A circle $K$ is inscribed in a quarter circle with radius 6 as shown in the figure. What is the radius of circle $K$?
<image1>
|
MathVision
|
E
| |
706cbd86-5205-4bc8-b677-4f3750d40152
|
174
|
As shown in <image>,A parallelogram is divided into 4 triangles as shown in the figure. Of the following possibilities for the areas of the triangles at most one can be true. Which one is it?
<image1>
|
MathVision
|
A
| |
54534611-f779-4590-9406-6042374ea9d7
|
175
|
As shown in <image>,The figure shows graphs of functions $f$ and $g$ defined on real numbers. Each graph consists of two perpendicular halflines. Which equality is satisfied for every real number $x$?
<image1>
|
MathVision
|
C
| |
e2a09e44-344e-43a2-8aa4-da49bb3a12c6
|
176
|
As shown in <image>,How many triangles can be drawn with vertices in the 18 points shown in the figure?
<image1>
|
MathVision
|
711
| |
b6c959c5-f47f-45dd-8144-b414267e505d
|
177
|
As shown in <image>,Let $A B C D$ be a convex quadrilateral with an area of 1 where $A B$ and $B D$ are the bases of two isosceles triangles $A D B$ and $B C D$ respectively (as shown). The product $A C \cdot B D$ is equal to:
<image1>
|
MathVision
|
D
| |
c5118fa7-2758-4c7f-bb2c-a5835d68a951
|
178
|
As shown in <image>,Five cards are lying on the table in the order 1,3,5,4,2. You must get the cards in the order $1,2,3,4,5$. Per move, any two cards may be interchanged. How many moves do you need at least?
<image1>
|
MathVision
|
2
| |
4304b7cc-aae7-49ce-9ffc-3d81c62778f6
|
179
|
As shown in <image>,A square piece of paper has been cut in three pieces. Two of them are in the picture on the right. What is the third one?
<image1>
<image2>
|
MathVision
|
A
| |
b400e4a3-e753-4ae4-996b-62fa899981d7
|
180
|
As shown in <image>,A $3 \times 3 \times 3$ cube weighs 810 grams. If we drill three holes through it as shown, each of which is a $1 \times 1 \times 3$ rectangular parallelepiped, the weight of the remaining solid is:
<image1>
|
MathVision
|
C
| |
c34a1033-175f-46b0-a51a-23911c809b6c
|
181
|
As shown in <image>,We are given three semi-circles as shown. $A B E F$ is a rectangle and the radius of each of the semi-circles is $2 \mathrm{~cm}$. $E$ and $F$ are the centers of the bottom semi-circles. The area of the shaded region (in $\mathrm{cm}^{2}$) is:
<image1>
|
MathVision
|
8
| |
e7281efa-e89f-43ad-ac35-dfec569d9d4b
|
182
|
As shown in <image>,The diagram shows a rectangle $A B E F$ and a triangle $A B C$. We know that the angle $A C F$ equals angle $C B E$. If $F C=6$ and $C E=2$ then the area of $A B C$ is:
<image1>
|
MathVision
|
D
| |
9489c375-39bd-42b0-951c-f3de7cb91fdc
|
183
|
As shown in <image>,In the quadrilateral $A B C D$ the diagonal $B D$ is the bisector of $\angle A B C$ and $A C=B C$. Given $\angle B D C=80^{\circ}$ and $\angle A C B=20^{\circ}, \angle B A D$ is equal to:
<image1>
|
MathVision
|
D
| |
25651404-cc44-4acc-af2b-5667b319ec2a
|
184
|
As shown in <image>,We consider the perimeter and the area of the region corresponding to the grey squares. How many more squares can we colour grey for the grey area to increase without increasing its perimeter?
<image1>
|
MathVision
|
16
| |
7b31eaf6-9269-4c60-9000-6a2ab3d53479
|
185
|
As shown in <image>,There are four cards on the table as in the picture. Every card has a letter on one side and a number on the other side. Peter said: "For every card on the table it is true that if there is a vowel on one side, there is an even number on the other side." What is the smallest number of cards Alice must turn in order to check whether Peter said the truth?
<image1>
|
MathVision
|
2
| |
e313d760-8f79-49a8-b274-b05795155929
|
186
|
As shown in <image>,Susan has two pendants made of the same material. They are equally thick and weigh the same. One of them has the shape of an annulus created from two concentric circles with the radii $6 \mathrm{~cm}$ and $4 \mathrm{~cm}$ (see the diagram). The second has the shape of a solid circle. What is the radius of the second pendant?
<image1>
|
MathVision
|
D
| |
79a91e5f-4198-4ca5-bc08-a4680e511f8c
|
187
|
As shown in <image>,In the diagram, $A B$ has length $1 ; \angle A B C=\angle A C D=90^{\circ}$; $\angle C A B=\angle D A C=\theta$. What is the length of $A D$?
<image1>
|
MathVision
|
E
| |
a5ef6604-8f1e-4589-97cf-d778dba7df1b
|
188
|
As shown in <image>,The radius of the traffic sign is $20 \mathrm{~cm}$. Each of the dark pieces is a quarter of a circle. The area of all 4 quarters equals that of the light part of the sign. What is the radius of this circle in centimetres?
<image1>
|
MathVision
|
A
| |
bed51092-6815-485c-9a0b-c83091f471f4
|
189
|
As shown in <image>,The ratio of the radii of the sector and the incircle in the picture is $3: 1$. Than the ratio of their areas is:
<image1>
|
MathVision
|
A
| |
cb68a5fa-1bfd-45cb-8e1e-5c46656f6dc1
|
190
|
As shown in <image>,The cells of a $4 \times 4$ table are coloured black and white as shown in the left figure. One move allows us to exchange any two cells positioned in the same row or in the same column. What is the least number of moves necessary to obtain in the right figure?
<image1>
|
MathVision
|
4
| |
fe95382a-5d36-4c0d-87a2-ebc5f8b95d1c
|
191
|
As shown in <image>,In a church there is a rose window as in the figure, where the letters R, G and B represent glass of red colour, green colour and blue colour, respectively. Knowing that $400 \mathrm{~cm}^{2}$ of green glass have been used, how many $\mathrm{cm}^{2}$ of blue glass are necessary?
<image1>
|
MathVision
|
400
| |
188fd44f-795e-4a5f-91e5-c2e75b8da6b1
|
192
|
As shown in <image>,The lengths of the sides of triangle $X Y Z$ are $X Z=\sqrt{55}$, $X Y=8, Y Z=9$. Find the length of the diagonal $X A$ of the rectangular parallelepiped in the figure.
<image1>
|
MathVision
|
10
| |
1c045f36-e210-43c4-b186-0d5bb84d8cec
|
193
|
As shown in <image>,Points $M$ and $N$ are given on the sides $A B$ and $B C$ of a rectangle $A B C D$. Then the rectangle is divided into several parts as shown in the picture. The areas of 3 parts are also given in the picture. Find the area of the quadrilateral marked with "?".
<image1>
|
MathVision
|
25
| |
6afc44bc-d8b0-4303-b1d9-9e9dc26d8613
|
194
|
As shown in <image>,In how many ways can all the numbers $1,2,3,4,5,6$ be written in the squares of the figure (one in each square) so that there are no adjacent squares in which the difference of the numbers written is equal to 3? (Squares that share only a corner are not considered adjacent.)
<image1>
|
MathVision
|
A
| |
8c6ca848-d4c1-43e5-aa1d-bdb1cb2f6e9f
|
195
|
As shown in <image>,A die is in the position shown in the picture. It can be rolled along the path of 12 squares as shown. How many times must the die go around the path in order for it to return to its initial position with all faces in the initial positions?
<image1>
|
MathVision
|
3
| |
5c0a907c-08ba-442a-9eaf-5d87d10d898d
|
196
|
As shown in <image>,If each side of the regular hexagon has length $\sqrt{3}$ and $X A B C$ and $X P Q R$ are squares, what is the area of the shaded region?
<image1>
|
MathVision
|
A
| |
d0f40601-1c1d-49e0-855e-267f2975a799
|
197
|
As shown in <image>,The shaded area is equal to $\sqrt{3}$. What is the area of the triangle $A B C$?
<image1>
|
MathVision
|
A
| |
d828a24b-d947-45a3-b44a-488c59fc498e
|
198
|
As shown in <image>,The billiard ball meets the board under $45^{\circ}$ as shown. Which pocket will it fall into?
<image1>
|
MathVision
|
C
| |
087da52e-a0ec-442f-9833-aa305f5d4dfb
|
199
|
As shown in <image>,The segment $A E$ is divided into four equal parts and semicircles are drawn taking $A E, A D$ and $D E$ as diameters, creating two paths from $A$ to $E$ as shown. Determine the ratio of the length of the upper path to the length of the lower path.
<image1>
|
MathVision
|
E
| |
e45f09fe-edca-4d4d-adf9-2d2cb89c038e
|
200
|
As shown in <image>,A mathematically skilled spider spins a cobweb and some of the strings have lengths as shown in the picture. If $x$ is an integer, determine the value of $x$.
<image1>
|
MathVision
|
13
|
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