Datasets:

mathvision
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mathvision

id stringlengths 1 4	question stringlengths 41 533	options sequencelengths 0 5	image stringlengths 12 15	answer stringclasses 48 values	solution stringclasses 26 values	level int64 1 5	subject stringclasses 16 values
4	How many different digits can you find in this picture? <image1>	[]	images/4.jpg	6	null	1	counting
5	Which number do you have to write in the last daisy? <image1>	[]	images/5.jpg	61	null	2	arithmetic
6	Misty the cat has five kittens: two of them are striped, one spotty, the rest of them are absolutely white. In which picture can we see the kittens of Misty, knowing that the ears of one of them are of different colour? <image1>	[ "A", "B", "C", "D", "E" ]	images/6.jpg	D	null	3	logic
7	How many bricks are missing in the wall? <image1>	[]	images/7.jpg	6	null	1	counting
8	The sums of the all the three numbers on each side of the triangle are equal. Two numbers happened to be stained with ink. How much is the sum of these two numbers? <image1>	[]	images/8.jpg	2	null	2	arithmetic
10	Four people can be seated at a square table. How many people at most could be seated if we pushed four tables of this kind together in one row? <image1>	[]	images/10.jpg	10	null	2	arithmetic
11	Mike has built a construction, shown in the upper picture, from equal cubes. Lily has taken several cubes out of it, thus Mike's construction became such as we see in the lower picture. How many cubes has Lily taken? <image1>	[]	images/11.jpg	7	null	1	solid geometry
16	How many points are there in the three unseen sides of dice? <image1>	[]	images/16.jpg	11	null	2	arithmetic
20	How many plums (see the picture) weigh as much as an apple? <image1>	[]	images/20.jpg	3	null	2	arithmetic
23	Tom bought a chocolate heart (see the picture) to Mary on her birthday. <image1> How many grams did the chocolate weigh, if each square weighs 10 grams?	[]	images/23.jpg	140	null	1	combinatorial geometry
26	The ladybird would like to sit on his flower. The flower has five petals and the stem has three leaves. On which flower should the ladybird sit? <image1>	[ "A", "B", "C", "D", "E" ]	images/26.jpg	B	null	1	counting
27	Theresa moves a pencil along the line. She starts at the arrow shown. In which order will she go past the shapes? <image1>	[ "$\\Delta, \\square, \\bullet$", "$\\Delta, \\bullet, \\square$", "$\\bullet, \\Delta, \\square$", "$\\square, \\Delta, \\bullet$", "$\\square, \\bullet, \\Delta$" ]	images/27.jpg	A	null	5	topology
28	There are more grey squares than white. How many more? <image1>	[]	images/28.jpg	9	null	1	counting
29	A big square is made from 25 small squares put together. A few of the small squares have been lost. How many have been lost? <image1>	[]	images/29.jpg	10	null	1	counting
32	The kangaroo is inside how many circles? <image1>	[]	images/32.jpg	3	null	1	counting
33	When the ant <image1> walks from home <image2> along the arrows $\rightarrow 3, \uparrow 3, \rightarrow 3, \uparrow 1$, he gets to the ladybird <image3>. Which animal does the ant <image1> get to when he walks from home <image2> along the following arrows: $\rightarrow 2, \downarrow 2, \rightarrow 3, \uparrow 3, \rightarrow 2, \uparrow 2$? <image6> <image7>	[ "A", "B", "C", "D", "E" ]	images/33.jpg	A	null	2	analytic geometry
34	Max has cut a rectangle into two pieces. One piece looks like: <image1> What does the other piece look like? <image2>	[ "A", "B", "C", "D", "E" ]	images/34.jpg	E	null	1	combinatorial geometry
35	Seven sticks lay on top of each other. Stick 2 lays right at the bottom. Stick 6 lays right on top. Which stick lays exactly in the middle? <image1>	[]	images/35.jpg	3	null	2	descriptive geometry
38	Each of the digits 2, 3, 4 and 5 will be placed in a square. Then there will be two numbers, which will be added together. What is the biggest number that they could make? <image1>	[]	images/38.jpg	95	null	2	arithmetic
39	Ingrid has 4 red, 3 blue, 2 green and 1 yellow cube. She uses them to build the following object: <image1> Cubes with the same colour don't touch each other. Which colour is the cube with the question mark?	[ "red", "blue", "green", "Yellow", "This cannot be worked out for certain." ]	images/39.jpg	A	null	3	logic
41	How many triangles can you find in the picture? <image1>	[]	images/41.jpg	5	null	1	counting
43	How many dots do all ladybirds have together? <image1>	[]	images/43.jpg	19	null	1	counting
44	Florian has 10 equally long metal strips with equally many holes. <image1> He bolts the metal strips together in pairs. Now he has five long strips (see the diagram). <image2> Which of the long strips is the shortest?	[ "A", "B", "C", "D", "E" ]	images/44.jpg	B	null	1	counting
45	Which of the kangaroo cards shown below can be turned around so that it then looks the same as the card shown on the right? <image1> <image2>	[ "A", "B", "C", "D", "E" ]	images/45.jpg	E	null	2	transformation geometry
46	What do you see if you look at the tower, which is made up of two building blocks, exactly from above? <image1> <image2>	[ "A", "B", "C", "D", "E" ]	images/46.jpg	A	null	2	descriptive geometry
49	Every one of these six building blocks consists of 5 little cubes. The little cubes are either white or grey. Cubes of equal colour don't touch each other. How many little white cubes are there in total? <image1>	[]	images/49.jpg	12	null	1	solid geometry
50	Which piece is missing? <image1> <image2>	[ "A", "B", "C", "D", "E" ]	images/50.jpg	A	null	2	transformation geometry
52	Which point in the labyrinth can we get to, starting at point $O$? <image1>	[ "A", "B", "C", "D", "E" ]	images/52.jpg	C	null	1	graph theory
53	Max has 10 dice. Which one of the following solids can he build with them? <image1>	[ "A", "B", "C", "D", "E" ]	images/53.jpg	A	null	1	combinatorial geometry
55	Gerda walks along the road and writes down the letters she can see on her right hand side. Which word is formed while Gerda walks from point 1 to point 2? <image1>	[ "KNAO", "KNGO", "KNR", "AGRO", "KAO" ]	images/55.jpg	A	null	1	combinatorics
58	<image1> In the picture above five ladybirds can be seen. Each one is sitting on a certain flower. A ladybird is only allowed to sit on a flower if the following conditions are met: 1) The difference between the number of points on each wing is equal to the number of leaves on the stem. 2) The number of points on the wings of the ladybird is equal to the number of petals on the flower. Which of the following flowers is without a ladybird? <image2>	[ "A", "B", "C", "D", "E" ]	images/58.jpg	E	null	3	logic
59	<image1> In the picture above we see a cube in two different positions. The six sides of the cube look like this: <image2> Which side is opposite to <image3>? <image4>	[]	images/59.jpg	C	null	1	solid geometry
60	Ellen wants to decorate the butterfly Which butterfly can she make? <image1> using these 6 stickers <image2> <image3>	[ "A", "B", "C", "D", "E" ]	images/60.jpg	A	null	1	combinatorial geometry
61	Into how many pieces will the string be cut? <image1>	[]	images/61.jpg	9	null	1	counting
62	How many blocks are missing in this igloo? <image1>	[]	images/62.jpg	10	null	1	counting
63	This picture shows a bracelet with pearls. <image1> Which of the bands below shows the same bracelet as above? <image2>	[ "A", "B", "C", "D", "E" ]	images/63.jpg	E	null	5	topology
64	Four of the numbers 1,3,4,5 and 7 are written into the boxes so that the calculation is correct. Which number was not used? <image1>	[]	images/64.jpg	4	null	2	arithmetic
65	Jim and Ben are sitting in a ferris wheel (see picture on the right). The ferris wheel is turning. Now Ben is in the position where Jim was beforehand. Where is Jim now? <image1> <image2>	[ "A", "B", "C", "D", "E" ]	images/65.jpg	C	null	2	transformation geometry
66	Alfred turns his building block 10 times. The first three times can be seen in the picture. What is the final position of the building block? <image1> <image2>	[ "A", "B", "C", "D", "E" ]	images/66.jpg	D	null	2	transformation geometry
71	Each one of the four keys locks exactly one padlock. Every letter on a padlock stands for exactly one digit. Same letters mean same digits. Which letters must be written on the fourth padlock? <image1>	[ "GDA", "ADG", "GAD", "GAG", "DAD" ]	images/71.jpg	D	null	3	logic
75	Peter has drawn this pattern: <image1> He draws exactly the same pattern once more. Which point is on his drawing?	[ "A", "B", "C", "D", "E" ]	images/75.jpg	D	null	1	combinatorial geometry
78	In order to get to his bone, the dog has to follow the black line. In total he turns 3-times to the right and 2-times to the left. Which path does he take? <image1>	[ "A", "B", "C", "D", "E" ]	images/78.jpg	E	null	1	counting
79	Lisa needs exactly 3 pieces to complete her jigsaw. Which of the 4 pieces is left over? <image1> <image2>	[ "A", "B", "C", "D", "C or D" ]	images/79.jpg	A	null	1	combinatorial geometry
80	Charles cuts a rope into 3 equally long pieces. Then he makes one knot in one of the pieces, 2 in the next and in the third piece 3 knots. Then he lays the three pieces down in a random order. Which picture does he see? <image1>	[ "A", "B", "C", "D", "E" ]	images/80.jpg	B	null	1	metric geometry - length
86	Which of the 5 pictures shows a part of this chain? <image1> <image2>	[ "A", "B", "C", "D", "E" ]	images/86.jpg	C	null	1	combinatorial geometry
89	Jörg is sorting his socks. Two socks with the same number are one pair. <image1> How many pairs can he find?	[]	images/89.jpg	5	null	1	counting
90	Five equally big square pieces of card are placed on a table on top of each other. The picture on the side is created this way. The cards are collected up from top to bottom. In which order are they collected? <image1>	[ "5-4-3-2-1", "5-2-3-4-1", "5-4-2-3-1", "5-3-2-1-4", "5-2-3-1-4" ]	images/90.jpg	E	null	2	descriptive geometry
91	The floor of a room is covered with equally big rectangular tiles (see picture). How long is the room? <image1>	[ "$6 \\mathrm{~m}$", "$8 \\mathrm{~m}$", "$10 \\mathrm{~m}$", "$11 \\mathrm{~m}$", "$12 \\mathrm{~m}$" ]	images/91.jpg	E	null	1	combinatorial geometry
92	The picture shows a mouse and a piece of cheese. The mouse is only allowed to move to the neighbouring fields in the direction of the arrows. How many paths are there from the mouse to the cheese? <image1>	[]	images/92.jpg	6	null	1	combinatorics
93	Which of the figures can be cut into these 3 pieces? <image1> <image2>	[ "A", "B", "C", "D", "E" ]	images/93.jpg	C	null	1	combinatorial geometry
95	There are white, grey and black squares. Three children use these to make this pattern. <image1> First Anni replaces all black squares with white squares. Then Bob replaces all grey squares with black squares. Finally Chris replaces all white squares with grey squares. Which picture have the three children now created? <image2>	[ "A", "B", "C", "D", "E" ]	images/95.jpg	A	null	1	combinatorial geometry
99	Julia has 5 pieces of plastic and has stacked these pieces on a table, as shown beside. What was the second piece she put on the table? <image1> <image2>	[ "A", "B", "C", "D", "E" ]	images/99.jpg	C	null	2	descriptive geometry
100	Marco's father took a picture of his son in front of the car shown beside. Which of the drawings below could represent this picture? <image1> <image2>	[ "A", "B", "C", "D", "E" ]	images/100.jpg	E	null	2	descriptive geometry
104	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>	[]	images/104.jpg	2	null	1	solid geometry
105	Ana draws some shapes on a sheet. Her drawing has fewer squares than triangles. What could be her drawing? <image1>	[ "A", "B", "C", "D", "E" ]	images/105.jpg	D	null	1	counting
107	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>	[ "On A", "On B", "On C", "On D", "On E" ]	images/107.jpg	D	null	3	logic
110	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>	[ "A", "B", "C", "D", "E" ]	images/110.jpg	B	null	2	descriptive geometry
114	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>	[]	images/114.jpg	8	null	1	algebra
115	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>	[]	images/115.jpg	3	null	3	logic
117	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>	[ "Person A", "Person B", "Person C", "Person D", "Person E" ]	images/117.jpg	C	null	3	logic
118	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>	[]	images/118.jpg	16	null	1	combinatorics
120	The picture shows 2 mushrooms. What is the difference between their heights? <image1>	[]	images/120.jpg	5	null	2	arithmetic
123	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>	[ "A", "B", "C", "D", "E" ]	images/123.jpg	A	null	2	descriptive geometry
124	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>	[]	images/124.jpg	6	null	1	counting
125	In the Kangaroo constellation, all stars have a number greater than 3 and their sum is 20 . Which is the Kangaroo constellation? <image1>	[ "A", "B", "C", "D", "E" ]	images/125.jpg	B	null	2	arithmetic
126	Edmund cut a ribbon as shown in the picture. How many pieces of the ribbon did he finish with? <image1>	[]	images/126.jpg	12	null	5	topology
130	Which figure can be made from the 2 pieces shown on the right? <image1> <image2>	[ "A", "B", "C", "D", "E" ]	images/130.jpg	A	null	1	combinatorial geometry
131	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>	[ "A", "B", "C", "D", "E" ]	images/131.jpg	B	null	3	logic
133	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>	[ "A", "B", "C", "D", "E" ]	images/133.jpg	A	null	1	algebra
149	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?	[]	images/149.jpg	9	null	1	algebra
152	The picture shows 5 cubes from the front. What do they look like from above? <image1> <image2>	[ "A", "B", "C", "D", "E" ]	images/152.jpg	B	null	2	descriptive geometry
157	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>	[ "A", "B", "C", "D", "E" ]	images/157.jpg	B	null	2	transformation geometry
159	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?	[]	images/159.jpg	3	null	1	algebra
162	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>	[ "A", "B", "C", "D", "E" ]	images/162.jpg	C	null	3	logic
164	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>	[ "154", "100", "90", "88", "60" ]	images/164.jpg	A	null	5	algebra
167	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>	[]	images/167.jpg	248	null	5	algebra
168	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>	[]	images/168.jpg	75	null	5	metric geometry - area
173	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>	[ "$\\frac{6-\\sqrt{2}}{2}$", "$\\frac{3 \\sqrt{2}}{2}$", "2.5", "3", "$6(\\sqrt{2}-1)$" ]	images/173.jpg	E	null	5	metric geometry - length
175	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>	[ "$f(x)=-g(x)+2$", "$f(x)=-g(x)-2$", "$f(x)=-g(x+2)$", "$f(x+2)=-g(x)$", "$f(x+1)=-g(x-1)$" ]	images/175.jpg	C	null	4	analytic geometry
176	How many triangles can be drawn with vertices in the 18 points shown in the figure? <image1>	[]	images/176.jpg	711	null	5	combinatorics
180	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>	[ "$540 \\mathrm{~g}$", "$570 \\mathrm{~g}$", "$600 \\mathrm{~g}$", "$630 \\mathrm{~g}$", "$660 \\mathrm{~g}$" ]	images/180.jpg	C	null	3	solid geometry
181	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>	[]	images/181.jpg	8	null	5	metric geometry - area
183	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>	[ "$90^{\\circ}$", "$100^{\\circ}$", "$110^{\\circ}$", "$120^{\\circ}$", "$135^{\\circ}$" ]	images/183.jpg	D	null	4	metric geometry - angle
187	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>	[ "$\\cos \\beta+\\tg \\beta$", "$\\frac{1}{\\cos (2 \\beta)}$", "$\\cos ^{2} \\beta$", "$\\cos (2 \\beta)$", "$\\frac{1}{\\cos ^{2} \\beta}$" ]	images/187.jpg	E	null	5	metric geometry - length
190	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>	[]	images/190.jpg	4	null	5	graph theory
193	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>	[]	images/193.jpg	25	null	5	metric geometry - area
195	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>	[]	images/195.jpg	3	null	3	solid geometry
201	Two semicircles are drawn as shown in the figure. The chord $C D$, of length 4 , is parallel to the diameter $A B$ of the greater semicircle and touches the smaller semicircle. Then the area of the shaded region equals <image1>	[ "$\\pi$", "$1.5 \\pi$", "$2 \\pi$", "$3 \\pi$", "Not enough data" ]	images/201.jpg	C	null	5	metric geometry - area
203	We see in the diagram at the right a piece of the graphic of the function $$ f(x)=a x^{3}+b x^{2}+c x+d. $$ What is the value of $b$? <image1>	[]	images/203.jpg	-2	null	4	analytic geometry
206	A river starts at point $A$. As it flows the river splits into two. The first branch takes $\frac{2}{3}$ of the water and the second takes the rest. Later the first branch splits into three, one taking $\frac{1}{8}$ of the branch's water, the second $\frac{5}{8}$ and the third one the rest. Further down this last branch meets again a branch of the river. The map below shows the situation. What part of the original water flows at point $B$? <image1>	[ "$\\frac{1}{3}$", "$\\frac{5}{4}$", "$\\frac{2}{9}$", "$\\frac{1}{2}$", "$\\frac{1}{4}$" ]	images/206.jpg	D	null	5	graph theory
210	We take three points from the grid so that they were collinear. How many possibilities do we have? <image1>	[]	images/210.jpg	20	null	5	combinatorics
211	In the figure each asterisk stands for one digit. The sum of the digits of the product is equal to <image1>	[]	images/211.jpg	16	null	5	algebra
213	The square $A B C D$ has a side of length 1 and $M$ is the midpoint of $A B$. The area of the shaded region is <image1>	[ "$\\frac{1}{24}$", "$\\frac{1}{16}$", "$\\frac{1}{8}$", "$\\frac{1}{12}$", "$\\frac{2}{13}$" ]	images/213.jpg	D	null	5	metric geometry - area
214	We used metal rods to build this nice ensemble. We know there are 61 octagons. How many rods are there? <image1>	[]	images/214.jpg	446	null	5	algebra
215	The suare in the diagram has side length 1. The radius of the small circle would then be of the length <image1>	[ "$\\sqrt{2}-1$", "$\\frac{1}{4}$", "$\\frac{\\sqrt{2}}{4}$", "$1-\\frac{\\sqrt{2}}{2}$", "$(\\sqrt{2}-1)^{2}$" ]	images/215.jpg	E	null	5	metric geometry - length
216	Each side of a triangle $A B C$ is being extended to the points $\mathrm{P}, \mathrm{Q}, \mathrm{R}, \mathrm{S}, \mathrm{T}$ and $\mathrm{U}$, so that $\mathrm{PA}=\mathrm{AB}=\mathrm{BS}, \mathrm{TC}=\mathrm{CA}$ $=\mathrm{AQ}$ and $\mathrm{UC}=\mathrm{CB}=\mathrm{BR}$. The area of $\mathrm{ABC}$ is 1. How big is the area of the hexagon PQRSTU? <image1>	[]	images/216.jpg	13	null	5	metric geometry - area
217	In the diagram on the right we want to colour the fields with the colours A, B, C and D so that adjacent fields are always in different colours. (Even fields that share only one corner, count as adjacent.) Some fields have already been coloured in. In which colour can the grey field be coloured in? <image1>	[ "either A or B", "only C", "only D", "either C or D", "A, B, C or D" ]	images/217.jpg	D	null	5	graph theory
218	A (very small) ball is kicked off from point A on a square billiard table with side length $2 \mathrm{~m}$. After moving along the shown path and touching the sides three times as indicated, the path ends in point $B$. How long is the path that the bal travels from A to B? (As indicated on the right: incident angle = emergent angle.) <image1>	[ "7", "$2 \\sqrt{13}$", "8", "$4 \\sqrt{3}$", "$2 \\cdot(\\sqrt{2}+\\sqrt{3})$" ]	images/218.jpg	B	null	5	metric geometry - length
219	In the diagram to the right a $2 \times 2 \times 2$ cube is made up of four transparent $1 \times 1 \times 1$ cubes and four non-transparent black $1 \times 1 \times 1$ cubes. They are placed in a way so that the entire big cube is nontransparent; i.e. looking at it from the front to the back, the right to the left, the top to the bottom, at no point you can look through the cube. What is the minimum number of black $1 \times 1 \times 1$ cubes needed to make a $3 \times 3 \times 3$ cube non-transparent in the same way? <image1>	[]	images/219.jpg	9	null	3	solid geometry
222	In the diagram on the right we see the birdô-eye view and front elevation of a solid that is defined by flat surfaces (i.e. view from obove and the front respectively). Bird' s-Eye View (view from above): <image1>. Front Elevation (view from the front): <image2>. Which of the outlines I to IV can be the side elevation (i.e. view from the left) of the same object? <image3>	[ "I", "II", "III", "IV", "none of them" ]	images/222.jpg	D	null	1	descriptive geometry

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Measuring Multimodal Mathematical Reasoning with MATH-Vision Dataset

[Homepage] [ArXiv Paper] [Huggingface Dataset] [Github]

Data usage

from datasets import load_dataset

dataset = load_dataset("mathvision/mathvision")
print(dataset)

Introduction

Recent advancements in Large Multimodal Models (LMMs) have shown promising results in mathematical reasoning within visual contexts, with models approaching human-level performance on existing benchmarks such as MathVista. However, we observe significant limitations in the diversity of questions and breadth of subjects covered by these benchmarks. To address this issue, we present the MATH-Vision (MATH-V) dataset, a meticulously curated collection of 3,040 high-quality mathematical problems with visual contexts sourced from real math competitions. Spanning 16 distinct mathematical disciplines and graded across 5 levels of difficulty, our dataset provides a comprehensive and diverse set of challenges for evaluating the mathematical reasoning abilities of LMMs.

Levels, subjects and sources distribution of MATH-V.

Through extensive experimentation, we unveil a notable performance gap between current LMMs and human performance on MATH-V, underscoring the imperative for further advancements in LMMs.

The accuracies of four prominent Large Multimodal Models (LMMs), random chance, and human performance are evaluated on our proposed MATH-Vision (MATH-V) across 16 subjects. Human performance is assessed using the testmini subset.

Moreover, our detailed categorization allows for a thorough error analysis of LMMs, offering valuable insights to guide future research and development.

Error distribution of 232 GPT-4V wrong results on the testmini subset of MATH-V.

You can refer to the project homepage and the paper for more details.

Dataset Examples

Some examples of MATH-V on three subjects: analytic geometry, topology, and graph theory.

Analytic geometry

Topology

Graph Geometry

You can refer to the Appendix D.3 of the paper for example images of 16 subjects.

🏆 Leaderboard

Accuracy scores on the test set (3,040 examples):

#	Model	Method	Date	ALL	Alg	AnaG	Ari	CombG	Comb	Cnt	DescG	GrphT	Log	Angle	Area	Len	SolG	Stat	Topo	TransG
1	GPT-4V	LMM (Text+Image)	2024-02-22	22.76	27.3	32.1	35.7	21.1	16.7	13.4	22.1	14.4	16.8	22.0	22.2	20.9	23.8	24.1	21.7	25.6
2	Gemini Pro	LMM (Text+Image)	2024-02-22	17.66	15.1	10.7	20.7	20.1	11.9	7.5	20.2	21.1	16.8	19.1	19.0	20.0	14.3	13.8	17.4	20.8
3	Qwen-VL-Max	LMM (Text+Image)	2024-02-22	15.59	10.7	19.1	20.0	16.9	12.5	17.9	16.4	12.2	21.0	13.3	14.2	19.8	11.5	20.7	13.0	17.3
4	InternLM-XComposer2-VL	LMM (Text+Image)	2024-02-22	14.54	9.3	15.5	12.1	15.3	11.3	10.5	14.4	22.2	19.3	19.7	15.6	15.0	11.9	15.5	26.1	15.5
5	SPHINX-MoE	LMM (Text+Image)	2024-02-22	14.18	7.8	17.9	14.3	15.6	9.5	11.9	12.5	15.6	12.6	16.2	15.6	17.8	13.5	12.1	8.7	16.1
6	GPT-4-CoT	LLM (Text+Image Caption)	2024-02-22	13.10	16.5	20.2	34.3	10.4	17.9	19.4	7.7	11.1	10.1	9.8	9.6	9.1	13.5	13.8	8.7	12.5
7	ShareGPT4V-13B	LMM (Text+Image)	2024-02-22	11.88	7.5	15.5	16.4	10.7	8.9	9.0	11.5	8.9	7.6	11.6	13.0	17.4	10.3	8.6	8.7	12.5
8	LLaVA-v1.5-13B	LMM (Text+Image)	2024-02-22	11.12	7.0	14.3	14.3	9.1	6.6	6.0	13.5	5.6	13.5	10.4	12.6	14.7	11.5	13.8	13.0	10.7
9	Qwen-VL-Plus	LMM (Text+Image)	2024-02-22	10.72	11.3	17.9	14.3	12.7	4.8	10.5	15.4	8.9	14.3	11.6	6.4	10.0	14.3	6.9	8.7	11.31
10	ShareGPT4V-7B	LMM (Text+Image)	2024-02-22	10.53	5.5	3.6	12.9	10.1	4.8	7.5	11.5	14.4	10.9	16.2	11.8	12.3	9.8	15.5	17.4	11.3
11	ChatGPT-3.5-CoT	LLM (Text+Image Caption)	2024-02-22	9.74	10.7	20.0	18.6	10.1	7.7	17.9	16.4	10.0	13.5	6.4	5.8	6.5	9.4	12.1	4.4	10.7
12	SPHINX (V2)	LMM (Text+Image)	2024-02-22	9.70	6.7	7.1	12.9	7.5	7.7	6.0	9.6	16.7	10.1	11.0	11.8	12.5	8.2	8.6	8.7	6.0
13	LLaVA-v1.5-7B	LMM (Text+Image)	2024-02-22	8.52	7.0	7.1	10.7	7.1	4.8	10.5	7.7	10.0	9.2	15.6	10.2	9.8	5.3	8.6	4.4	4.8
14	GPT-4-CoT	LLM (Text)	2024-02-22	8.16	12.8	10.7	15.7	4.9	10.7	10.5	1.9	5.6	8.4	8.1	6.2	8.7	8.6	3.5	4.4	4.8
15	Random Chance	-	2024-02-22	7.17	1.5	11.9	7.1	9.7	4.8	6.0	22.1	1.1	7.6	0.6	9.4	6.7	8.2	8.6	13.0	7.1

Accuracy scores on the testmini subset (304 examples):

#	Model	Method	Date	ALL	Alg	AnaG	Ari	CombG	Comb	Cnt	DescG	GrphT	Log	Angle	Area	Len	SolG	Stat	Topo	TransG
-	Human	-	2024-02-22	75.66	57.9	79.0	100.0	100.0	47.4	94.7	89.5	63.2	63.2	36.8	52.6	73.7	89.5	89.5	100.0	73.7
1	GPT-4V	LMM (Text+Image)	2024-02-22	22.37	26.3	31.6	36.8	21.1	15.8	10.5	21.1	15.8	15.8	21.1	21.1	21.1	26.3	26.3	21.1	26.3
2	Gemini Pro	LMM (Text+Image)	2024-02-22	17.11	15.8	10.5	21.1	21.1	10.5	5.3	21.1	21.1	15.8	21.1	21.1	21.1	15.8	15.8	15.8	21.1
3	Qwen-VL-Max	LMM (Text+Image)	2024-02-22	16.1	10.5	21.1	21.1	15.8	15.8	15.8	15.8	21.1	10.5	15.8	10.5	21.1	15.8	15.8	10.5	15.8
4	InternLM-XComposer2-VL	LMM (Text+Image)	2024-02-22	15.79	10.5	15.8	10.5	15.8	10.5	10.5	15.8	21.1	21.1	21.1	15.8	15.8	10.5	15.8	26.3	15.8
5	SPHINX-MoE	LMM (Text+Image)	2024-02-22	13.49	10.5	15.8	15.8	15.8	10.5	10.5	10.5	15.8	10.5	15.8	15.8	10.5	10.5	15.8	15.8	15.8
6	ShareGPT4V-13B	LMM (Text+Image)	2024-02-22	13.49	15.8	21.1	10.5	5.3	15.8	10.5	15.8	10.5	15.8	36.8	21.1	5.3	10.5	5.3	10.5	5.3
7	LLaVA-v1.5-13B	LMM (Text+Image)	2024-02-22	13.10	10.4	5.3	15.8	5.3	10.5	10.5	26.3	5.3	15.8	31.6	10.5	15.8	15.8	10.5	15.8	10.5
8	GPT-4-CoT	LLM (Text+Image Caption)	2024-02-22	12.50	15.8	10.5	31.6	5.3	15.8	31.6	10.5	15.8	15.8	0.0	5.3	5.3	0.0	21.1	10.5	5.3
9	ShareGPT4V-7B	LMM (Text+Image)	2024-02-22	12.50	5.3	0.0	10.5	21.1	5.3	5.3	26.3	15.8	15.8	15.8	10.5	21.1	15.8	15.8	10.5	5.3
10	Qwen-VL-Plus	LMM (Text+Image)	2024-02-22	10.53	26.3	10.5	10.5	15.8	10.5	21.1	5.3	10.5	10.5	10.5	5.3	5.3	0.0	0.0	0.0	0.0
11	ChatGPT-3.5-CoT	LLM (Text+Image Caption)	2024-02-22	10.20	10.5	26.3	5.3	0.0	10.5	21.1	15.8	10.5	0.0	10.5	0.0	5.3	21.1	5.3	10.5	5.3
12	LLaVA-v1.5-7B	LMM (Text+Image)	2024-02-22	10.20	0.0	10.5	15.8	5.3	5.3	15.8	10.5	10.5	15.8	21.1	15.8	15.8	5.3	10.5	0.0	5.3
13	Random Chance	-	2024-02-22	9.87	0.0	15.8	10.5	15.7	0.0	0.0	36.84	0.0	15.8	0.0	10.5	21.1	5.3	10.5	15.8	0.0
14	SPHINX (V2)	LMM (Text+Image)	2024-02-22	9.21	5.3	10.5	10.5	0.0	21.1	10.5	10.5	15.8	10.5	15.8	5.3	10.5	0.0	5.3	5.3	10.5
15	GPT-4-CoT	LLM (Text)	2024-02-22	6.58	5.3	10.5	15.8	0.0	21.1	10.5	5.3	0.0	5.3	10.5	5.3	0.0	5.3	5.3	5.3	0.0

Note: Subjects: Alg: algebra, AnaG: analytic geometry, Ari: arithmetic, CombG: combinatorial geometry, Comb: combinatorics, Cnt: counting, DescG: descriptive geometry, GrphT: graph theory, Log: logic, Angle: metric geometry - angle, Area: metric geometry - area, Len: metric geometry-length, SolG: solid geometry, Stat: statistics, Topo: topology, TransG: transformation geometry.

ChatGPT-3.5: the gpt-3.5-turbo-0125 engine. GPT-4: the gpt-4-0125-preview engine. GPT-4V: the gpt-4-1106-vision-preview engine. Human: the average score of 30 college or master students recruited.

Citation

If you find this benchmark useful in your research, please consider citing this BibTex:

@misc{wang2024measuring,
      title={Measuring Multimodal Mathematical Reasoning with MATH-Vision Dataset}, 
      author={Ke Wang and Junting Pan and Weikang Shi and Zimu Lu and Mingjie Zhan and Hongsheng Li},
      year={2024},
      eprint={2402.14804},
      archivePrefix={arXiv},
      primaryClass={cs.CV}
}

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