Datasets:

CauchyFan
/

UNREAL_Benchmark

id stringlengths 9 9	index int32 1 600	qtype stringclasses 2 values	domain stringclasses 5 values	subdomain stringclasses 16 values	question stringlengths 40 703	answer stringlengths 1 166	options stringlengths 2 1.13k	source_image stringlengths 13 13
MATH_0001	1	oe	Mathematics	metric_geometry	In the sandy arrangement, twelve congruent disks are placed on a circle $C$ of radius 1 such that the disks cover $C$, no two disks overlap, and each disk is tangent to its two neighbors. The sum of the areas of the twelve disks can be written in the form $\pi(a-b\sqrt{c})$, where $a, b, c$ are positive integers and $c...	135	{}	MATH_0001.png
MATH_0002	2	oe	Mathematics	metric_geometry	In the stone garden layout, hexagon $ABCDEF$ is partitioned into regions $\mathcal{P, Q, R, S,}$ and $\mathcal{T}$. The regions $\mathcal{P, Q, R,}$ and $\mathcal{S}$ are congruent rhombuses, each with area $\sqrt{2006}$. Let $K$ be the area of rhombus $\mathcal{T}$. Given that $K$ is a positive integer, find the numbe...	89	{}	MATH_0002.png
MATH_0003	3	oe	Mathematics	metric_geometry	In the vintage desk photo, square $ABCD$ has points $E, F, G, H$ on sides $AB, BC, CD, DA$ respectively. Segments $EG$ and $FH$ intersect at $P$ such that $EG \perp FH$ and $EG = FH = 34$. The areas of the quadrilaterals $AEPH, BFPE, CGPF,$ and $DHPG$ (labeled $w, x, y, z$ in the diagram) are in the ratio $269:275:405:...	850	{}	MATH_0003.png
MATH_0004	4	oe	Mathematics	metric_geometry	Two externally tangent circles $\omega_1$ and $\omega_2$ are centered at $O_1$ and $O_2$. A third circle $\Omega$ passes through $O_1$ and $O_2$, intersecting $\omega_1$ at points $B$ and $C$ and $\omega_2$ at points $A$ and $D$. Given that $AB = 2$, $O_1O_2 = 15$, and $CD = 16$, and that $ABO_1CDO_2$ forms a convex he...	140	{}	MATH_0004.png
MATH_0005	5	oe	Mathematics	metric_geometry	On the sketched paper, a square has side length 2. Semi-circles are centered at the corners and pass through the square's midpoint. Grey circles are centered on the sides and touch the semi-circles. What is the total area of the grey regions?	$4 \cdot(3-2 \sqrt{2}) \cdot \pi$	{}	MATH_0005.png
MATH_0006	6	oe	Mathematics	metric_geometry	In the perspective sketch, the diagram indicates a scheme for associating points on segment $ \overline{AB}$ with those on segment $ \overline{A'B'}$. Analytically, let $ x$ be the distance from a point $ P$ on $ \overline{AB}$ to $ D$, and let $ y$ be the distance from the associated point $ P'$ on $ \overline{A'B'}$ ...	$17 - 3a$	{}	MATH_0006.png
MATH_0007	7	oe	Mathematics	metric_geometry	In the rusty pipeline diagram, consider the layout forming $ riangle ABC$, where $E$ is the midpoint of side $BC$ and $D$ lies on side $AC$. Given that the length of $AC$ is $1$ and the angles are $\measuredangle BAC = 60^\circ$, $\measuredangle ABC = 100^\circ$, $\measuredangle ACB = 20^\circ$, and $\measuredangle DEC...	$\frac{\sqrt{3}}{8}$	{}	MATH_0007.png
MATH_0008	8	oe	Mathematics	metric_geometry	In the diagram, $AB \perp BC$, $BC \perp CD$, and $BC$ is tangent to the circle with center $O$ and diameter $AD$. Determine the lengths of $AB$ and $CD$ for which the area of $ABCD$ is an integer.	AB=9, CD=4	{}	MATH_0008.png
MATH_0009	9	oe	Mathematics	metric_geometry	In the green knitted texture, the displayed decagon has adjacent sides meeting at right angles. Calculate its perimeter.	44	{}	MATH_0009.png
MATH_0010	10	oe	Mathematics	metric_geometry	Maria runs to the underground, exits after two stops, and subsequently walks the rest of the way by foot to school. Which of the speed-time diagrams below best describes her journey?	D	{}	MATH_0010.png
MATH_0011	11	oe	Mathematics	metric_geometry	In the denim embroidery, there are eleven circles with four distinct radii. The circles labelled $W$ have radius 1, each circle labelled $X$ has radius 2, the circle labelled $Y$ has radius 4, and the circle labelled $Z$ has radius $r$. Every circle marked $W$ or $X$ is tangent to three other circles. The circle marked...	25538, 2053	{}	MATH_0011.png
MATH_0012	12	oe	Mathematics	metric_geometry	In the mosaic diagram, lines $AC$ and $DF$ are tangent to the circle at $B$ and $E$. The line $AF$ cuts the circle at $P$ and $R$ and intersects $BE$ at $Q$. If $\angle CAF = 35^{\circ}$, $\angle DFA = 30^{\circ}$, and $\angle FPE = 25^{\circ}$, find the measure of $\angle PEQ$.	32.5	{}	MATH_0012.png
MATH_0013	13	oe	Mathematics	metric_geometry	In the stone mosaic diagram, $A B C D$ and $P N C D$ are squares with side length 2, where $P N C D$ is perpendicular to $A B C D$. Point $M$ is placed on the same side of $P N C D$ as $A B$ such that $ riangle P M N$ is parallel to $A B C D$, $\angle P M N=90^{\circ}$, and $P M=M N$. Calculate the volume of the convex...	\frac{16}{3}	{}	MATH_0013.png
MATH_0014	14	oe	Mathematics	solid_geometry	In the industrial render, a cube has a side length of 18 cm. A giant ant crawls along the yellow piping from X to Y. What is the total distance traveled?	$90 \mathrm{~cm}$	{}	MATH_0014.png
MATH_0015	15	oe	Mathematics	solid_geometry	In the drafting sketch, the two diagrams display a perspective view and a plan view of a tower constructed from light and dark blocks. Within the tower, dark blocks rest exclusively on dark blocks, and light blocks rest exclusively on light blocks. Determine the total count of light-coloured blocks.	20	{}	MATH_0015.png
MATH_0016	16	oe	Mathematics	solid_geometry	In the wooden crate assembly, a large block is constructed using small cubes of identical size. The exterior surface is completely red, while the interior cubes are blue. How many blue cubes are hidden inside?	12	{}	MATH_0016.png
MATH_0017	17	oe	Mathematics	solid_geometry	In the purple crystal arrangement, the structure is built from identical cubes and weighs 189 grams in total. Find the weight of a single cube.	21	{}	MATH_0017.png
MATH_0018	18	oe	Mathematics	solid_geometry	In the golden field, a fortress is constructed from cubes. Determine the total number of cubes used to build the structure.	56	{}	MATH_0018.png
MATH_0019	19	oe	Mathematics	solid_geometry	In the wooden block setup, a pyramid is constructed from cubes. Each cube has a side length of $10 \mathrm{~cm}$. An ant travels along the red line marked on the structure. What is the total length of the ant's path?	$90 \mathrm{~cm}$	{}	MATH_0019.png
MATH_0020	20	oe	Mathematics	solid_geometry	On the blueprint paper, Maria possesses exactly 9 white cubes, 9 light gray cubes, and 9 dark gray cubes, all identical in size. She assembles them into a single larger cube. Identify which of the displayed cubes corresponds to her creation.	A	{}	MATH_0020.png
MATH_0021	21	oe	Mathematics	solid_geometry	On the sketched napkin, which of the labeled shapes can be produced by rotating the grey object in space?	W and Y	{}	MATH_0021.png
MATH_0022	22	oe	Mathematics	solid_geometry	In the vine-covered diagram, a beetle crawls along the edges of a cube. Starting from point $P$, it moves in the direction indicated. At the end of every edge, it alternates its turn direction: first right, then left, then right, and so forth. How many edges will it travel along before it gets back to point $P$?	6	{}	MATH_0022.png
MATH_0023	23	oe	Mathematics	solid_geometry	In the desk photo, a large cube with side length 3 is formed by 15 black and 12 white unit cubes. Five of the six faces of this cube are visible in the top sequence. Identify which option below corresponds to the remaining sixth face.	A	{}	MATH_0023.png
MATH_0024	24	oe	Mathematics	solid_geometry	Mike starts with 125 identical small cubes. He assembles a large cube structure that features exactly nine tunnels passing straight all the way through. Calculate the number of cubes from the original 125 that are left unused.	39	{}	MATH_0024.png
MATH_0025	25	oe	Mathematics	solid_geometry	In the denim schematic, a net of a rectangular box is laid out. Calculate the volume of the box in $\mathrm{cm}^{3}$.	80	{}	MATH_0025.png
MATH_0026	26	oe	Mathematics	descriptive_geometry	In the leafy checkered scene, which of the cubes labeled A through E corresponds to the folded version of the central net?	E	{}	MATH_0026.png
MATH_0027	27	oe	Mathematics	descriptive_geometry	In the sandy scene, four identical dice are stacked to form a tower as shown. The sum of the numbers on opposite faces of each die is always 7. Which option depicts the tower as seen from behind?	C	{}	MATH_0027.png
MATH_0028	28	oe	Mathematics	descriptive_geometry	In the soil etching, a floral design is drawn on the inside of a window. Which option shows how the flowers look when viewed from the outside?	E	{}	MATH_0028.png
MATH_0029	29	oe	Mathematics	descriptive_geometry	In the castle scene, a rectangular banner is partially hidden by a wooden board. The hidden part is a	triangle	{}	MATH_0029.png
MATH_0030	30	oe	Mathematics	descriptive_geometry	Five children each have a black square, a grey triangle, and a white circle made of paper. The children stack the three shapes as seen in the pictures. In how many images was the triangle placed after the square?	3	{}	MATH_0030.png
MATH_0031	31	oe	Mathematics	descriptive_geometry	In the industrial port scene, Max builds a structure using identical containers. The clipboard displays the overhead plan, showing the number of containers in each stack. What is the sum of the numbers obscured by the two hearts?	5	{}	MATH_0031.png
MATH_0032	32	oe	Mathematics	descriptive_geometry	In the wooden block scene, Janaína assembled a structure using light-colored and darker cubes. Which grid pattern represents the top-down view of her construction?	B	{}	MATH_0032.png
MATH_0033	33	oe	Mathematics	descriptive_geometry	In the mossy stone engraving, a net is carved. If cut, folded, and glued to form a cube, which of the cubes below could be the result?	A	{}	MATH_0033.png
MATH_0034	34	oe	Mathematics	descriptive_geometry	In the sandy beach scene, John uses building blocks to form a work of art. Which of the patterns (A, B, C, D, E from left to right) represents the view from above?	C	{}	MATH_0034.png
MATH_0035	35	oe	Mathematics	descriptive_geometry	In the camouflaged concrete diagram, a corner has been removed from a cube. Which of the shown nets represents the unfolded surface of the resulting solid?	E	{}	MATH_0035.png
MATH_0036	36	oe	Mathematics	descriptive_geometry	In the warehouse layout, Johann places $1 \times 1$ cubes on a $4 \times 4$ grid. The numbers in the grid indicate the stack height for each square. What profile does Johann see when viewing the structure from the rear (hinten)?	(C)	{}	MATH_0036.png
MATH_0037	37	oe	Mathematics	descriptive_geometry	In the dockside arrangement, a builder wants to form a cube using these numbered crates. Since there are 7 crates instead of the 6 required faces, determine which crate(s) can be removed so the remaining 6 stay connected and create a valid cube net.	only 3 or 7	{}	MATH_0037.png
MATH_0038	38	oe	Mathematics	descriptive_geometry	In the concrete block rendering, three geometric blocks are arranged on a surface. Which of the options represents the view from directly above?	C	{}	MATH_0038.png
MATH_0039	39	oe	Mathematics	descriptive_geometry	In the sandcastle diagram, John built a structure with identical cubes, using the maximum number to match the three views displayed. Ana wishes to remove as many cubes as possible without changing these views. What is the maximum number of cubes she can remove?	12	{}	MATH_0039.png
MATH_0040	40	oe	Mathematics	transformation_geometry	In the rusty metal layout, two squares share the same center $O$ and have side lengths of 1. If the length of segment $\overline{AB}$ is $43/99$, find the area of octagon $ABCDEFGH$ in the form $m/n$, where $m$ and $n$ are relatively prime positive integers, and compute $m+n$.	185	{}	MATH_0040.png
MATH_0041	41	oe	Mathematics	transformation_geometry	In the metallic 3D visualization, an equilateral triangle rolls along the perimeter of a unit square. Determine the total length of the path traced by the red vertex, assuming the triangle rolls until both the shape and the vertex return to their initial positions for the first time.	$\frac{28}{3} \pi$	{}	MATH_0041.png
MATH_0042	42	oe	Mathematics	transformation_geometry	In the chalk sketch, a rectangular paper strip $ABCD$ is $5 \mathrm{~cm}$ wide and $50 \mathrm{~cm}$ long, white on one side and grey on the other. The strip is folded so that vertex $B$ meets $M$, the midpoint of edge $CD$. Then, it is folded again so that vertex $D$ meets $N$, the midpoint of edge $AB$. Determine the...	$60 \mathrm{~cm}^{2}$	{}	MATH_0042.png
MATH_0043	43	oe	Mathematics	transformation_geometry	In the rusty metal sign graphic, the word KANGAROO is displayed on a clear sheet. Which option represents the view after flipping the sheet over its back along the right-hand side edge and then turning it $180^{\circ}$ on the table?	E	{}	MATH_0043.png
MATH_0044	44	oe	Mathematics	transformation_geometry	In the textured grid layout, one of the wooden segments is the result of rotating the other. Determine which of the points $T, U, V$, $W$ could act as the center of rotation.	either of $U$ and $W$	{}	MATH_0044.png
MATH_0045	45	oe	Mathematics	combinatorial_geometry	In the mossy stone carving, a square slab was cut into three pieces. Two of them are visible at the top. Which labeled option below is the third piece?	A	{}	MATH_0045.png
MATH_0046	46	oe	Mathematics	combinatorial_geometry	In the concrete enclosure, there are seven shipping containers. You want to rearrange the containers so that another container can be placed. What is the minimum number of containers that have to be moved?	3	{}	MATH_0046.png
MATH_0047	47	oe	Mathematics	combinatorial_geometry	In the mug grid layout, let $S=\{(x,y) : x \in \{0,1,2,3,4\}, y \in \{0,1,2,3,4,5\}$, and $(x,y) \neq (0,0) \}$. Let $T$ denote the set of all right triangles with vertices chosen from $S$. For every right triangle $t=\triangle ABC$ where vertices $A$, $B$, and $C$ are in counter-clockwise order and the right angle is ...	$\frac{625}{144}$	{}	MATH_0047.png
MATH_0048	48	oe	Mathematics	combinatorial_geometry	In the aerial grid layout, 3 of the unit squares have been shaded. What is the minimum number of additional unit squares that must be shaded so that the resulting figure possesses two lines of symmetry?	7	{}	MATH_0048.png
MATH_0049	49	oe	Mathematics	combinatorial_geometry	In the concrete tray display, a rectangular board has length $2^{2014}$ and height $3^{2014}$, divided into unit squares. A termite starts at the left or bottom edge, walking along gridlines only right or up until reaching the opposite edge. This path cuts the board into two sections. Sammy discovers these sections can...	4	{}	MATH_0049.png
MATH_0050	50	oe	Mathematics	combinatorial_geometry	In the grassy field rendering, consider the rectangle $R$ in the Cartesian plane with vertices at $(0,0), (2,0), (2,1),$ and $(0,1)$. As shown, $R$ is split into two unit squares, creating a figure with seven edges. Find the number of subsets of these seven edges that form a connected figure.	81	{}	MATH_0050.png
MATH_0051	51	oe	Mathematics	combinatorial_geometry	In the grassy field layout, let $R$ be the rectangle defined by vertices $(0,0), (2,0), (2,1),$ and $(0,1)$. As illustrated, $R$ is split into two unit squares, resulting in a figure with seven edges. Find the number of ways to pick one or more of these seven edges such that the selected edges can be traced without lif...	61	{}	MATH_0051.png
MATH_0052	52	oe	Mathematics	combinatorial_geometry	In the mossy diorama, which pair of cube structures from the choices below fits together to build the object shown at the top?	A	{}	MATH_0052.png
MATH_0053	53	oe	Mathematics	combinatorial_geometry	In the stone courtyard grid, what is the minimum number of small squares that must be shaded to create an axis of symmetry?	3	{}	MATH_0053.png
MATH_0054	54	oe	Mathematics	combinatorial_geometry	In the mossy forest scene, an L-shaped figure composed of four squares is shown. Determine the number of ways to attach one additional square of the same size such that the resulting shape possesses a line of symmetry.	3	{}	MATH_0054.png
MATH_0055	55	oe	Mathematics	combinatorial_geometry	In the dark rock carving, a straight line connects a vertex of the left triangle to a vertex of the right triangle such that the segment does not dissect either triangle. In how many ways is this possible?	4	{}	MATH_0055.png
MATH_0056	56	oe	Mathematics	combinatorial_geometry	In the blueprint layout, the figure labeled side 1 is formed by six equal triangles made with 12 sticks. How many sticks are needed to complete the figure labeled side 2, partially represented?	36	{}	MATH_0056.png
MATH_0057	57	oe	Mathematics	combinatorial_geometry	In the overhead cargo layout, Carl attempts to partition the large crate formation into smaller sections using only replicas of the T-piece and the F-piece displayed on the right. (Sections can be rotated or flipped.) What is the minimum number of T-pieces required?	2	{}	MATH_0057.png
MATH_0058	58	oe	Mathematics	combinatorial_geometry	In the hedge maze diagram, the lawnmower is programmed to move in a straight line. If it encounters a hedge (shown by the thick green borders), it turns right by $90^{\circ}$ and continues straight. If it cannot go straight or turn right, it will stop. What will happen to this lawnmower?	It will never stop.	{}	MATH_0058.png
MATH_0059	59	oe	Mathematics	combinatorial_geometry	In the wooden crate layout, what is the minimum number of extra crates we must paint red for the entire arrangement to exhibit a line of symmetry?	3	{}	MATH_0059.png
MATH_0060	60	oe	Mathematics	combinatorial_geometry	In the overhead container view, a square enclosure measures $5 \mathrm{~cm}$ by $5 \mathrm{~cm}$. Seven bars, each $1 \mathrm{~cm}$ by $3 \mathrm{~cm}$, are inside. Kanga plans to slide the bars to accommodate one additional bar. What is the minimum number of bars Kanga must move?	3	{}	MATH_0060.png
MATH_0061	61	oe	Mathematics	graph_theory	In the angled photograph, the cells of a $4 \times 4$ table are colored black and white as seen in the left grid. One move permits exchanging any two cells situated in the same row or column. What is the fewest number of moves needed to produce the pattern in the right grid?	4	{}	MATH_0061.png
MATH_0062	62	oe	Mathematics	graph_theory	The diagram shows a steampunk network of fourteen brass chambers connected by pipes. A total of 3360 coins are initially placed among the chambers. Two chambers are considered adjacent if they are directly connected by a pipe. Simultaneously, each chamber sends away all of its coins, dividing them equally among its adj...	280	{}	MATH_0062.png
MATH_0063	63	oe	Mathematics	graph_theory	On the antique desk, color the grid fields using A, B, C, and D such that adjacent fields (including those touching at a corner) always have different colors. Given the pre-filled squares on the paper, which color is valid for the grey field?	either C or D	{}	MATH_0063.png
MATH_0064	64	oe	Mathematics	graph_theory	In the mossy camouflage graph, the weight of a path is defined as the sum of the numbers on its edges. Determine the minimum weight for a path that visits every vertex exactly once.	65	{}	MATH_0064.png
MATH_0065	65	oe	Mathematics	graph_theory	In the cupcake tray setup, consider a $5 imes 5$ grid split into 25 slots. Initially, all slots contain white-frosted cupcakes. In each move, it is allowed to change the frosting color of three slots that are adjacent in a horizontal or vertical line (i.e., white turns to chocolate and chocolate turns to white). What ...	less than 10	{}	MATH_0065.png
MATH_0066	66	oe	Mathematics	graph_theory	In the metallic honeycomb structure, a bee named Maja plans to hike from honeycomb $X$ to honeycomb $Y$. Movement is permitted only between adjacent honeycombs that share an edge. Determine the number of distinct paths from $X$ to $Y$ that visit each of the seven honeycombs exactly once.	5	{}	MATH_0066.png
MATH_0067	67	oe	Mathematics	graph_theory	In the concrete pipe grid, fill each square with one of the symbols P, Q, R, or S so that no two neighboring squares have the same symbol. (Squares sharing a corner are neighbors.) Based on the current layout, which symbol(s) can go in the grey square?	either R or S	{}	MATH_0067.png
MATH_0068	68	oe	Mathematics	graph_theory	The image shows a pink cellular maze with two crystalline gates and sixteen berry-like nutrient clusters placed on the network. A path may move only along the raised cellular corridors, and each junction may be visited at most once. Starting from one crystalline gate and ending at the other, what is the greatest number...	13	{}	MATH_0068.png
MATH_0069	69	oe	Mathematics	graph_theory	In the jungle canopy diagram, Peter colors each of the eight circles red, yellow, or blue. Circles connected by a vine cannot be the same color. Which two circles must Peter color identically?	5 and 8	{}	MATH_0069.png
MATH_0070	70	oe	Mathematics	graph_theory	In the diagram on the paper, each of the eight circles is colored red, yellow, or blue such that no two directly connected circles share the same color. Which pair of circles is guaranteed to have the same color?	5 and 8	{}	MATH_0070.png
MATH_0071	71	oe	Mathematics	graph_theory	In the swampy network, the large central lily pad is labeled Sarah, and the twenty smaller lily pads are connected by moss-covered paths. A virus begins on Sarah’s lily pad and spreads only along the mossy paths. In the first round, it infects every smaller lily pad directly connected to Sarah; in the second round, it ...	6	{}	MATH_0071.png
MATH_0072	72	oe	Mathematics	graph_theory	In the swampy network, the large central lily pad is labeled Sarah, and the twenty smaller lily pads are connected by moss-covered paths. A virus begins on Sarah’s lily pad and spreads only along the mossy paths. In the first round, it infects every smaller lily pad directly connected to Sarah; in the second round, it ...	6	{}	MATH_0072.png
MATH_0073	73	oe	Mathematics	graph_theory	In the glowing root network, a map displays five settlements. Each settlement is intended to be connected to every other settlement by a path. The current layout is incomplete. How many paths are missing?	3	{}	MATH_0073.png
MATH_0074	74	oe	Mathematics	graph_theory	In the mossy stick layout, a kangaroo enters from the left. It moves exclusively through triangular rooms formed by the branches. Which exit letter does it reach?	E	{}	MATH_0074.png
MATH_0075	75	oe	Mathematics	graph_theory	In the camouflage maze layout, each square holds a piece of cheese. Ronnie the mouse plans to enter and leave the structure as shown. He must not visit any square more than once, yet he wants to consume as much cheese as possible. What is the maximum number of cheese pieces he can eat?	37	{}	MATH_0075.png
MATH_0076	76	oe	Mathematics	graph_theory	There is a river with two islands contains six bridges. Calculate the number of paths starting at point A and ending at point B that cross every bridge exactly one time.	6	{}	MATH_0076.png
MATH_0077	77	oe	Mathematics	combinatorial_geometry	In the camouflage diagram, a bracelet with pearls is depicted. Which of the bands below corresponds to the same bracelet shown above?	E	{}	MATH_0077.png
MATH_0078	78	oe	Mathematics	combinatorial_geometry	In the textured sketch, determine which of the figures are constructed from more than a single piece of string.	I, III and V	{}	MATH_0078.png
MATH_0079	79	oe	Mathematics	combinatorial_geometry	How many obvious gummies can be seen in gummy candies?	4	{}	MATH_0079.png
MATH_0080	80	oe	Mathematics	combinatorial_geometry	In the stone relief, identify which of the labeled figures are constructed from more than a single piece of string.	I, III and V	{}	MATH_0080.png
MATH_0081	81	oe	Mathematics	combinatorial_geometry	In the sand-etched diagram, a textured strip features five identical sections with distinct shapes as shown. The strip is folded so that all five sections stack into a single pile. Identify the stacking order, from the top layer down, that cannot be created.	A	{}	MATH_0081.png
MATH_0082	82	oe	Mathematics	combinatorics_counting	In the aerial garden view, Robin shoots three arrows at the target. Points are awarded for each shot based on the numbers displayed in the regions. If any arrow misses the target or if any two arrows land in adjacent regions, the total score is zero. How many distinct scores can he achieve?	13	{}	MATH_0082.png
MATH_0083	83	oe	Mathematics	combinatorics_counting	In the rustic wooden cabinet, a security system with ten numbered drawers opens when the correct five drawers are pulled in any order. The configuration shown has $\{1, 2, 3, 6, 9\}$ as its combination. If the system were modified to accept any set of drawers ranging from one to nine as a valid combination, how many ex...	770	{}	MATH_0083.png
MATH_0084	84	oe	Mathematics	combinatorics_counting	In the wooden grid tray, consider the $ 6\times4$ layout where $ 12$ of the $ 24$ compartments are to be shaded. The arrangement must satisfy the condition that there are exactly two shaded compartments in each row and three shaded compartments in each column. Let $ N$ represent the total number of such valid shadings....	860	{}	MATH_0084.png
MATH_0085	85	oe	Mathematics	combinatorics_counting	In the glass pawn grid, a $ 4\times4$ rectangular array of pieces is displayed, with each piece $ 1$ unit away from its nearest neighbors. Define a growing path as a sequence of distinct pieces where the distance between consecutive pieces strictly increases. Let $ m$ be the maximum number of pieces in a growing path, ...	240	{}	MATH_0085.png
MATH_0086	86	oe	Mathematics	combinatorics_counting	In the sketched castle layout, a structure features two concentric rings connected by five radial paths, with labels at every intersection. A traveler starts at point $A$ and moves between adjacent labeled points. Travel along the inner ring is strictly counterclockwise, while travel along the outer ring is strictly ...	4	{}	MATH_0086.png
MATH_0087	87	oe	Mathematics	combinatorics_counting	In the steampunk window grid, it displays 12 dots and 17 roads connecting certain pairs. Paula intends to travel along exactly 13 of those roads, starting at dot A and ending at dot L, without traveling along any portion of a road more than once. (Paula is allowed to visit a dot more than once.) How many different rout...	4	{}	MATH_0087.png
MATH_0088	88	oe	Mathematics	combinatorics_counting	In the steampunk grid, consider a $9 \times 9$ Sudoku array with entries from $\{1, 2, \ldots, 9\}$ satisfying the standard constraints that each row, column, and $3 \times 3$ box contains each digit exactly once. If a Sudoku matrix is selected uniformly at random, and two cells are fixed as depicted, find the probabil...	$\frac{2}{21}$	{}	MATH_0088.png
MATH_0089	89	oe	Mathematics	combinatorics_counting	In the concrete grid facade, the numbers $1,2, \ldots, 8$ are placed into the $3 \times 3$ grid, leaving exactly one square blank. A placement is valid if for any adjacent pair of squares, either one is blank or the difference between the numbers is at most 2 (squares are adjacent if they share a side). If rotations an...	32	{}	MATH_0089.png
MATH_0090	90	oe	Mathematics	combinatorics_counting	In the gothic courtyard, determine the number of distinct routes a king can take to travel from the top-left square to the bottom-right square of the grid using the minimum number of moves. (The king may move to any adjacent square, including those diagonally adjacent.)	4	{}	MATH_0090.png
MATH_0091	91	oe	Mathematics	combinatorics_counting	In the rustic window grid, a square $4 \times 4$ array is divided into 16 unit squares. Determine the maximum number of diagonals that can be drawn in these unit squares such that no two diagonals share any common point (including endpoints).	10	{}	MATH_0091.png
MATH_0092	92	oe	Mathematics	logic_constraints	In the wooden grid, certain compartments of the $4 \times 4$ layout must be marked black. The numbers stamped on the bottom and right sides specify how many cells in each column and row must be black. In how many ways can this arrangement be completed?	5	{}	MATH_0092.png
MATH_0093	93	oe	Mathematics	logic_constraints	In the sandy grid, to fill the table, every cell needs a 0 or 1, and each row and column must sum to 2. Find the values for $X$ and $Y$.	$X=0, Y=0$	{}	MATH_0093.png
MATH_0094	94	oe	Mathematics	logic_constraints	In the dried leaf diagram, each triangle's sides are colored blue, green, or red. Four sides are already labeled with colors as shown. Determine the possible color for the segment marked 'x', given that every triangle must have three distinct side colors.	only green	{}	MATH_0094.png
MATH_0095	95	oe	Mathematics	logic_constraints	In the mossy grid diagram, a number is placed in each square such that it equals the sum of the two numbers from adjacent squares (sharing an edge). Given the values 10 and 3 in the top corners, which number should be written in the square marked $x$?	7	{}	MATH_0095.png
MATH_0096	96	oe	Mathematics	logic_constraints	As shown in the figure, 5 cells and 3 paths are arranged as shown. A new cell is placed such that every path separates an equal number of cells on both sides. Which section will place the new cell?	B	{}	MATH_0096.png
MATH_0097	97	oe	Mathematics	logic_constraints	In the mossy stone carving, numbers must be written in each of the seven bounded regions. Regions are neighbors if they share a boundary. Each region's number is the sum of its neighbors' numbers. Two values are already shown: -4 and 2. Determine the number for the central region.	6	{}	MATH_0097.png
MATH_0098	98	oe	Mathematics	graph_theory	In the stone giant landscape, using a table of a certain height, two identical blocks are arranged. Length $r$ is $32$ inches. After rearranging the blocks, length $s$ is $28$ inches. How high is the table?	$30\text{ inches}$	{}	MATH_0098.png
MATH_0099	99	oe	Mathematics	graph_theory	In the industrial construction scene, three four-digit numbers are painted onto separate steel beams. The sum of these three numbers is 11126. Three of the digits are missing from the beams. Which three digits are hidden?	1,5 and 7	{}	MATH_0099.png
MATH_0100	100	oe	Mathematics	graph_theory	In the coffee bean arrangement, distinct letters represent distinct digits. Assuming the addition is valid, what is the maximum possible value for the sum C + A + N?	21	{}	MATH_0100.png

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UNREAL Benchmark

Visual reasoning across unfamiliar scenes
600 questions · 5 domains · Embedded images · English

UNREAL Benchmark is an evaluation dataset for visual question answering across mathematics, natural science, perception, physics and engineering, and reasoning and logic. Each example pairs an image with a question and a reference answer.

A look inside

Six examples from the released benchmark. Click any image to view it at full resolution. The gallery uses the original image bytes, with no cropping or retouching.

Physics & Engineering Reasoning about local gravity _{PHYS_0001}	Natural Science Anatomy and locomotion _{NATS_0001}
Mathematics Geometry in a visual scene _{MATH_0001}	Perception Spatial orientation and shadows _{PERC_0001}
Reasoning & Logic Recognizing anachronisms _{REAS_0001}	Reasoning & Logic Interpreting illumination _{REAS_0004}

Dataset at a glance

Domain	Examples
Mathematics	259
Natural Science	62
Perception	91
Physics & Engineering	96
Reasoning & Logic	92
Total	600

Question formats: 458 open-ended (oe) and 142 multiple-choice (mc).

The release contains three Parquet shards of 200 examples each. Images are embedded in the image column. The existing split name is train; the content is intended for evaluation.

Load the benchmark

from datasets import load_dataset

dataset = load_dataset("CauchyFan/UNREAL_Benchmark", split="train")
example = dataset[0]
print(example["id"], example["question"])
image = example["image"]  # PIL image

To iterate without downloading the entire release first:

stream = load_dataset(
    "CauchyFan/UNREAL_Benchmark", split="train", streaming=True
)
example = next(iter(stream))

Fields

Field	Description
`id`, `index`	Sample identifier and numeric index.
`domain`, `subdomain`	Topic labels.
`qtype`	`oe` for open-ended or `mc` for multiple-choice.
`question`, `answer`	Question text and reference answer.
`options`	JSON-encoded option mapping when present; parse with `json.loads`.
`option_map`	Human-readable labeled options when present.
`source_image`	Original image filename.
`image`	Embedded image decoded by Hugging Face Datasets.

For multiple-choice evaluation, present both the question and its labeled options. Keep reference answers separate from model inputs.

Genesis model family

Public checkpoints: Genesis-Qwen3vl-4B · Genesis-Qwen3vl-8B · Genesis-Qwen3vl-32B

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