Spatial and visual: open practice pack: learner worksheet

1. puz-spatial-and-visual-01: Turning the corner piece · Difficulty 1

The figure below is turned 90 degrees clockwise, staying flat on the page. Which description matches the result?

1. A bar across the top with an upright arm hanging from its left end
2. A bar across the top with an upright arm hanging from its right end
3. A bar across the bottom with an upright arm rising from its right end
4. An upright arm down the right-hand side with a bar across the bottom

Answer:

2. puz-spatial-and-visual-02: The mirrored floor plan · Difficulty 1

A room is drawn from above with north at the top. A desk stands against the north wall, towards the east corner; a door sits in the middle of the west wall. The plan is reflected in a mirror line running north to south down its middle. Where are the desk and the door in the reflected plan?

1. Desk against the north wall towards the east corner; door in the middle of the east wall
2. Desk against the south wall towards the east corner; door in the middle of the west wall
3. Desk against the north wall towards the west corner; door in the middle of the east wall
4. Desk against the south wall towards the west corner; door in the middle of the east wall

Answer:

3. puz-spatial-and-visual-03: Edges of the pointed solid · Difficulty 1

A solid has a square base, and four triangular sides that rise from the base and meet at a single point above it. How many edges does the solid have in total?

1. 4 edges
2. 8 edges
3. 5 edges
4. 12 edges

Answer:

4. puz-spatial-and-visual-04: Finishing the small square · Difficulty 1

In the two-by-two pattern below, the same change happens from left to right in each row. What belongs in the empty cell?

1. A circle with a dot inside it
2. A completely shaded square
3. A square with a dot just outside its top-right corner
4. A square with a dot inside it

Answer:

5. puz-spatial-and-visual-05: Squares inside the strip · Difficulty 1

How many squares of any size can be found in the figure below? Count the small cells and any larger squares that the cells form together.

1. 6 squares
2. 8 squares
3. 7 squares
4. 9 squares

Answer:

6. puz-spatial-and-visual-06: The card turned right round · Difficulty 2

A rectangular card has a small notch cut from its top-left corner and a hole punched near its bottom edge, slightly right of centre. The card is turned 180 degrees in its own plane; it is not flipped over. Where are the notch and the hole now?

1. Notch at the bottom-left corner; hole near the top edge, slightly right of centre
2. Notch at the top-right corner; hole near the bottom edge, slightly left of centre
3. Notch at the bottom-right corner; hole near the bottom edge, slightly left of centre
4. Notch at the bottom-right corner; hole near the top edge, slightly left of centre

Answer:

7. puz-spatial-and-visual-07: Which flat pattern makes a cube · Difficulty 2

Each description below is a flat arrangement of six identical squares joined edge to edge. Which one can be folded up into a closed cube?

1. A row of four squares, with one square attached above the second and one attached below the third
2. A row of four squares, with one square attached above the first and one attached above the second
3. A row of five squares, with one square attached above the second
4. Two rows of three squares, one row directly above the other

Answer:

8. puz-spatial-and-visual-08: The stacked cubes · Difficulty 2

Identical cubes are stacked in a corner. The bottom layer is a solid three-by-three square of cubes, a solid two-by-two square of cubes sits on top of that, and one single cube sits on top of those. No cube is missing from any layer. How many cubes are there altogether?

1. 6 cubes
2. 13 cubes
3. 14 cubes
4. 9 cubes

Answer:

9. puz-spatial-and-visual-09: Reflecting in the diagonal · Difficulty 2

Two counters sit on a three-by-three board: one in the top row, middle column; one in the bottom row, left column. The pattern is reflected in the diagonal running from the top-left corner to the bottom-right corner. Where are the counters afterwards?

1. Middle row left column, and bottom row left column
2. Bottom row middle column, and top row right column
3. Top row middle column, and bottom row right column
4. Middle row left column, and top row right column

Answer:

10. puz-spatial-and-visual-10: Two rows of boxes · Difficulty 2

One rule runs along each row of the figure below. What belongs in the empty box?

1. A box holding three circles
2. A box holding three crosses
3. A box holding four crosses
4. A box holding two crosses

Answer:

11. puz-spatial-and-visual-11: The shape that will not fold · Difficulty 2

Three of the shapes below can be folded along some straight line so that the two halves land exactly on each other. Which shape cannot?

1. A right-angled triangle whose two shorter sides have different lengths
2. A triangle with two sides of equal length
3. A rectangle twice as long as it is wide
4. A semicircle, made by cutting a disc along a diameter

Answer:

12. puz-spatial-and-visual-12: One fold, one punch · Difficulty 3

A square sheet is folded once, bringing the bottom edge up onto the top edge. A single hole is then punched through both layers, in the left half of the folded sheet and a little way above the fold. The sheet is unfolded flat. What do you see?

1. One hole only, in the left half, just above the horizontal centre line
2. Two holes the same distance above the centre line, one in the left half and one in the right half
3. Two holes in the left half, one just above and one just below the centre line, each the same distance from it
4. Two holes in the left half, both above the centre line, one near the top edge and one near the fold

Answer:

13. puz-spatial-and-visual-13: Two things change at once · Difficulty 3

Each step along a row changes the figure in two ways at once. The top row runs: a plain triangle, a shaded square, a plain pentagon. The bottom row runs: a plain square, a shaded pentagon, then a gap. What belongs in the gap?

1. A shaded hexagon
2. A plain pentagon
3. A shaded seven-sided shape
4. A plain hexagon

Answer:

14. puz-spatial-and-visual-14: Turning and swapping · Difficulty 3

A tile shows an arrow pointing up; its head is shaded and its tail is plain. Each move turns the tile a quarter turn clockwise and also swaps the shading, so whatever was shaded becomes plain and whatever was plain becomes shaded. What does the tile look like after three moves?

1. An arrow pointing left, with a plain head and a shaded tail
2. An arrow pointing left, with a shaded head and a plain tail
3. An arrow pointing right, with a plain head and a shaded tail
4. An arrow pointing down, with a plain head and a shaded tail

Answer:

15. puz-spatial-and-visual-15: Seen from the other side · Difficulty 3

Four posts stand in a straight line running east to west. Someone standing south of the line and facing it reads the posts from left to right as: striped, plain, notched, capped. Another person walks round to the north of the line and faces it. What do they read from left to right?

1. Striped, plain, notched, capped
2. Capped, notched, plain, striped
3. Striped, notched, plain, capped
4. Capped, plain, notched, striped

Answer:

16. puz-spatial-and-visual-16: Every rectangle in the grid · Difficulty 3

How many rectangles of any size can be found in the figure below? Count every rectangle, not only the ones that happen to be squares.

1. 8 rectangles
2. 11 rectangles
3. 30 rectangles
4. 20 rectangles

Answer:

17. puz-spatial-and-visual-17: The arrow on the folded wall · Difficulty 3

A flat cross of five squares makes an open box: a base square with one square joined to each of its four sides, folded up to form walls. On the flat cross, the square to the left of the base carries an arrow pointing away from the base, towards the left. Once the walls are folded upright, where does that arrow point?

1. Down towards the base of the box
2. Horizontally across the box, towards the opposite wall
3. Horizontally along the wall it is drawn on
4. Straight up, away from the base

Answer:

18. puz-spatial-and-visual-18: Two folds, one punch · Difficulty 4

A square sheet is folded in half, bottom edge up onto the top edge, then folded in half again, left edge across onto the right edge. One hole is punched through the folded packet, at the centre of the small square that results. The sheet is unfolded flat. What do you see?

1. Four holes, one at the centre of each quarter of the sheet
2. Two holes in the top half, one on each side of the vertical centre line
3. Two holes in the right half, one above and one below the horizontal centre line
4. One hole at the exact centre of the sheet

Answer:

19. puz-spatial-and-visual-19: Every shape once, every count once · Difficulty 4

In the matrix below, each row contains each of the three shapes exactly once and each of the three dot counts exactly once; the same is true of each column. What belongs in the empty cell?

1. A circle with one dot
2. A square with three dots
3. A square with one dot
4. A triangle with two dots

Answer:

20. puz-spatial-and-visual-20: Tipping and turning the cube · Difficulty 4

A cube sits with a star on top, a cross underneath, a circle facing you, a square on the far face, a triangle on the left and an arrow on the right. Tip it forward so the top face swings down onto the front, then turn it a quarter turn clockwise as seen from above. Which face is on top, and which faces you?

1. The star is on top and the arrow faces you
2. The square is on top and the arrow faces you
3. The square is on top and the triangle faces you
4. The circle is on top and the square faces you

Answer:

21. puz-spatial-and-visual-21: Three lines through a rectangle · Difficulty 4

A rectangle has both of its diagonals drawn, and also the straight line joining the midpoints of its left and right sides. Into how many separate regions is the inside of the rectangle divided?

1. 4 regions
2. 8 regions
3. 5 regions
4. 6 regions

Answer:

22. puz-spatial-and-visual-22: Walking the grid · Difficulty 4

You start on a square grid facing north. Walk forward three squares, turn right, walk two, turn right, walk three, turn left, walk one, turn left, walk two. Which way are you facing, and where are you relative to your starting square?

1. Facing north, three squares east and two squares north of the start
2. Facing east, three squares east and two squares north of the start
3. Facing north, two squares east and three squares north of the start
4. Facing south, three squares east and two squares north of the start

Answer:

23. puz-spatial-and-visual-23: The off-centre fold · Difficulty 5

A square sheet measures eight units by eight. Its left edge folds across to the right, with the crease three units from the left edge; the bottom edge then folds up onto the top edge. A hole is punched through every layer, two units in from the packet's left edge and two units above its foot. What do you see once the sheet is unfolded?

1. Two holes, both five units from the left edge, at heights of two and six units
2. Four holes: two of them one unit from the left edge and two of them five units from the left edge, each pair at heights of two and six units
3. Four holes: two of them three units from the left edge and two of them five units from the left edge, each pair at heights of two and six units
4. Four holes, all at a height of six units, one unit, three units, five units and seven units from the left edge

Answer:

24. puz-spatial-and-visual-24: Rows one way, shading the other · Difficulty 5

In the matrix below, one rule runs along the rows and a different rule governs the shading. What belongs in the empty cell?

1. A plain circle with five dots
2. A shaded circle with four dots
3. A shaded square with five dots
4. A shaded circle with five dots

Answer:

25. puz-spatial-and-visual-25: Turn then mirror · Difficulty 5

A tile shows an upright pole with a small flag attached at the top, sticking out to the right. The tile is first turned a quarter turn clockwise, and then reflected in a vertical mirror line. What does it show at the end?

1. A horizontal pole with its top end on the right and the flag standing up near that end
2. A horizontal pole with its top end on the right and the flag hanging below near that end
3. A horizontal pole with its top end on the left and the flag hanging below near that end
4. An upright pole with the flag at the top sticking out to the left

Answer: