Topic summaries
Analogies
Adding On: Plus Two Analogies
Pupils learn how analogy puzzles work by spotting that two symbols are added in both example pairs, then applying the same change to complete the last pair.
Analogies
Count and Shade
Pupils find a one-step change in shading through outline, solid, stripes and dots, and a one-step change in the number of small dots through 1 to 4, and apply both to the final figure.
Analogies
Inside Out: Swapping Inner and Outer
Pupils spot that the inner and outer shapes swap roles, with the new outer shape drawn as a large outline and the new inner shape as a small solid, and apply the swap to the last pair.
Analogies
Mirror Images: Vertical Reflection
Pupils recognise a reflection across a vertical mirror line, where left and right swap but top and bottom stay the same, and apply it to the whole final figure including its dot.
Analogies
Three Changes at Once
Pupils find three changes shown in both example pairs, drawn from direction, marker position, shading and dot count, and apply all three to the final figure.
Analogies
Turn and Fill
Pupils find two changes in both example pairs, a quarter-turn clockwise or anticlockwise and a change of fill to solid, and apply both to the final symbol.
Analogies
Turn and Jump: To the Opposite Side
Pupils separate two changes that happen at once, a 90-degree clockwise turn of the symbol and a dot jumping to the opposite side, and apply both to the final figure.
Analogies
Turns and Moving Markers
Pupils find two separate changes in the example pairs, a quarter-turn of direction and a one-side move of a perimeter marker, and apply both across a change of symbol.
Block Counting in 3D
Block Counting: Indented Arrangements
Pupils count deep, tall arrangements with an indented corner where no stack stands, recording zero for empty spots and adding every other stack once.
Block Counting in 3D
Block Counting: Solid Stepped Stacks
Pupils count the cubes in small stepped arrangements by treating each stack as a solid column, including the hidden cubes underneath the visible tops.
Block Counting in 3D
Block Counting: Varied Terraces
Pupils count taller terraced arrangements two stacks wide, counting each stack once and adding row by row, including all the cubes underneath the visible tops.
Block Counting in 3D
Block Counting: Wide Stepped Arrangements
Pupils count wider arrangements three stacks across, with nine or twelve stacks, using a grid of heights and row totals to reach totals of up to eighty.
Combining Shapes
Combining Shapes: Put Them Together
Pupils overlay two four-by-four grids and keep every square that is shaded in either grid, checking the result square by square.
Combining Shapes
Combining Shapes: Remove the Overlap
Pupils overlay two three-by-three grids without turning them and keep only the squares shaded in exactly one grid, removing any square shaded in both.
Combining Shapes
Combining Shapes: Take One Away
Pupils keep the squares shaded in the first grid but not the second, understanding that the order matters and that squares shaded only in the second grid never appear.
Combining Shapes
Combining Shapes: Turn, Then Combine
Pupils turn the second grid a quarter-turn anticlockwise, then overlay it on the first and remove squares shaded in both, following the instructions in order.
Cube Nets
Cube Nets: All Eleven Nets
Pupils find the opposite face across all eleven cube net shapes, including awkward staircase nets, and avoid choosing the queried face itself or one of its neighbours.
Cube Nets
Cube Nets: Faces at a Corner
Pupils use opposite pairs to find which three faces can meet at one corner of the folded cube, rejecting any triple that includes an opposite pair.
Cube Nets
Cube Nets: Finding the Opposite Face
Pupils learn what a cube net is and find the face opposite a given face, using the rules that opposite faces never share an edge and are one square apart in a straight line.
Cube Nets
Cube Nets: Two Opposites in Order
Pupils find the opposite faces for two queried faces and give them in the requested order, checking both answers because most wrong options get one of them right.
Extended Series: Hidden Panels
Hidden Panels: Shading and Dot Cycles
Pupils continue a long sequence with two covered panels, tracking a shading cycle and a dot-count cycle at every position, including wrapping round at the end of each cycle.
Extended Series: Hidden Panels
Hidden Panels: Three Changes at Once
Pupils identify three features that change at every position, from direction, marker position, shading and dot count, and continue all three past two covered panels to fill the final position.
Extended Series: Hidden Panels
Hidden Panels: Turning Arrows
Pupils find how far a symbol turns per position, 90 or 45 degrees clockwise or anticlockwise, and use it to fill the panel marked with a question mark, counting covered panels as positions.
Extended Series: Hidden Panels
Hidden Panels: Turns and Moving Markers
Pupils continue a long sequence with two covered panels, tracking a quarter-turn of direction and a one-side move of a perimeter marker at every position, hidden or not.
Figure Analysis: Folding and Punching
Folding and Punching: One Fold
Pupils fold a sheet once in one of four directions, punch it once, and find where both holes sit on the unfolded sheet by reflecting the punch across the crease.
Figure Analysis: Folding and Punching
Folding and Punching: Punches at Different Times
Pupils follow three folds with one punch made early and one made at the end, reflecting each punch only across the folds that existed when it was punched.
Figure Analysis: Folding and Punching
Folding and Punching: Two Folds, Four Holes
Pupils fold left onto right and then top onto bottom, punch once through all four layers, and unfold by reflecting across the horizontal and then the vertical crease.
Figure Analysis: Folding and Punching
Folding and Punching: Two Folds, Two Punches
Pupils follow two folds in varied directions and two punches made after both folds, undoing each fold in reverse order to find all eight holes.
Hidden Shapes
Hidden Shapes: Dense Line Networks
Pupils find long outlines hidden in dense networks with many extra lines, using a distinctive starting point and a careful edge count to separate the real outline from near misses.
Hidden Shapes
Hidden Shapes: Longer Irregular Outlines
Pupils find longer, irregular outlines with more segments hidden in line networks, breaking the outline into parts and checking every segment.
Hidden Shapes
Hidden Shapes: Stepped Outlines
Pupils find a stepped outline hidden in a grid of lines, keeping it the same size and orientation, and check that every segment of the outline is present.
Hidden Shapes
Hidden Shapes: Turned and Flipped Traps
Pupils find a four- or five-square outline hidden in a grid network at the same size and orientation, learning to reject networks that contain only a turned or flipped copy.
Horizontal Codes: Shapes to Letters
Cracking the Code: Direction and Marker Position
Pupils work out a two-letter code in which the first letter records direction and the second records marker position, by comparing references that differ in only one feature.
Horizontal Codes: Shapes to Letters
Cracking the Code: Shading and Dot Count
Pupils work out a two-letter code in which the first letter records shading and the second records the number of small dots, and build the code for the test figure.
Horizontal Codes: Shapes to Letters
Cracking the Code: Shape, Fill and Size
Pupils learn how letter codes work by finding that the first letter records shape, the second fill and the third size, then build the three-letter code for the test figure.
Horizontal Codes: Shapes to Letters
Cracking the Code: Three Features
Pupils crack three-letter codes in which each position records one of direction, marker position, shading or dot count, working out which position records which feature before building the test code.
Jigsaw: Fitting Pieces Together
Jigsaw: Eight-Square Targets
Pupils find the pair of four-square pieces that exactly makes an eight-square target, turning and moving the pieces but never flipping them, with no gaps or overlaps.
Jigsaw: Fitting Pieces Together
Jigsaw: Exact Fit
Pupils find the one pair of pieces that exactly tiles a varied eight-square target, using the target's outline and rejecting pairs that fit only if a piece is flipped.
Jigsaw: Fitting Pieces Together
Jigsaw: Ten-Square Targets
Pupils find the pair of five-square pieces that exactly makes a ten-square target, using the target's arms and corners to anchor the first piece.
Jigsaw: Fitting Pieces Together
Jigsaw: Twelve-Square Targets
Pupils find the pair of six-square pieces that exactly makes a twelve-square target with more inward corners, using anchors, elimination and careful checks for flips.
Matrices
Combine the Dots
Pupils find that the third panel in each row keeps every dot position from the first two panels, with shared positions appearing once, and apply this to complete the grid.
Matrices
One of Each: Fills in Every Row and Column
Pupils use the rule that each of three fills appears exactly once in every row and column to work out the missing fill, keeping the same shape.
Matrices
Remove the Overlaps
Pupils combine the first two patterns in each row and remove any positions that occur in both, leaving only the non-overlapping markers in the third panel.
Matrices
Rows and Columns: Counting in a Grid
Pupils learn how a matrix works by spotting that each row keeps its shape while the columns hold one, two, then three shapes, and use both rules to fill the missing box.
Matrices
Shading and Dots in a Grid
Pupils track a shading cycle and a dot-count cycle across each row, work out the separate steps down each column, and find the box where both routes agree.
Matrices
Three Rules in a Grid
Pupils track three changing features across rows and down columns, drawn from direction, marker position, shading and dot count, and find the box where both routes agree on all three.
Matrices
Turns and Markers in a Grid
Pupils track a quarter-turn of direction and a one-side move of a perimeter marker across each row, work out the separate steps down each column, and find the box where both routes agree.
Matrices
Two Kinds of Turn
Pupils find that moving right turns the symbol 90 degrees and moving down turns it 45 degrees, each clockwise or anticlockwise, and check that both routes agree on the missing box.
Most Like: Three Figures
Most Like: Matching Inner and Outer Shapes
Pupils learn how 'most like' puzzles work by finding that each example has matching inner and outer shapes with the same fills, and choosing the option that follows the same rule.
Most Like: Three Figures
Most Like: Shared Direction and Marker Position
Pupils find the direction and marker position that three examples share while other details vary, and choose the option that shares both.
Most Like: Three Figures
Most Like: Shared Shading and Dot Count
Pupils find the shading and number of small dots that three examples share while other details vary, and choose the option that shares both.
Most Like: Three Figures
Most Like: Three Shared Properties
Pupils work out which three properties the examples share, from direction, marker position, shading and dot count, and choose the option that shares all three.
Most Like: Two Figures
Two Clues: Matching Inner and Outer Shapes
Pupils work out from two examples that the inner and outer shapes match and the fills follow a pattern, then choose the option that follows the same rule.
Most Like: Two Figures
Two Clues: Shared Direction and Marker Position
Pupils compare two examples to find the direction and marker position they share, notice which details differ, and choose the option that shares both properties.
Most Like: Two Figures
Two Clues: Shared Shading and Dot Count
Pupils compare two examples to find the shading and number of small dots they share, ignore details that differ, and choose the option that shares both properties.
Most Like: Two Figures
Two Clues: Three Shared Properties
Pupils compare two examples across direction, marker position, shading and dot count to find the three they share, and choose the option that shares all three.
Odd One Out
Count the Sides
Pupils find that in four panels the number of markers equals the number of sides of the outer polygon, and spot the panel where the count is one out.
Odd One Out
Matching Halves: Vertical Symmetry
Pupils spot that four panels have matching left and right halves, and find the panel where one of the paired markers is lower than the other.
Odd One Out
Pointing the Right Way
Pupils find that four arrows or pointing symbols point towards their markers, and spot the one that does not.
Odd One Out
Shared Direction and Marker Position
Pupils find the direction and marker position that four figures share while other details vary, and spot the figure that breaks one of them.
Odd One Out
Shared Shading and Dot Count
Pupils find the shading and number of small dots that four figures share while other details vary, and spot the figure that breaks one of them.
Odd One Out
Solid and Outline Pairs
Pupils learn how odd-one-out puzzles work by spotting that four panels pair a solid shape with an outline shape, and finding the panel with two of the same.
Odd One Out
Three Shared Properties
Pupils work out which three properties four figures share, from direction, marker position, shading and dot count, and find the figure that breaks one of them.
Odd One Out
Turned or Flipped?
Pupils find that four figures match by turning them, and spot the one figure that is a mirror image and cannot match by rotation alone.
Sequences
Counting Up: Quantity Sequences
Pupils count the symbols in each panel, spot that one is added each time, and choose the panel that continues the count.
Sequences
Every Other Panel: Interleaved Sequences
Pupils separate two sequences that take turns in alternate panels and continue the count in the one the missing panel belongs to.
Sequences
On the Move: Position and Fill
Pupils track a marker moving one side around a frame each time while its shading alternates, and choose the panel where both rules continue.
Sequences
Quarter-Turns: Constant Rotation
Pupils spot a symbol turning 90 degrees clockwise or anticlockwise in every panel and choose the panel that continues the turn.
Sequences
Round and Round: Repeating Groups of Three
Pupils find a group of three shapes that repeats and use it to choose the panel that starts the group again.
Sequences
Shading and Dot Cycles
Pupils follow a shading cycle and a dot-count cycle, each running forwards or backwards and wrapping round, to choose the next panel.
Sequences
Three Rules at Once
Pupils track three features changing at the same time, drawn from direction, marker position, shading and dot count, and eliminate options rule by rule.
Sequences
Turns and Moving Markers
Pupils follow a direction that turns a quarter-turn and a perimeter marker that moves one side, keeping both rules going even when the symbol changes.
Shape Matching
Shape Matching: Curved Outlines
Pupils match smooth, curved outlines under turns and flips by comparing the order of bulges and dips around the edge, and rejecting options that change a substantial part of the silhouette.
Shape Matching
Shape Matching: Diagonal Outlines
Pupils match irregular outlines with diagonal edges and eight corners by comparing the sequence of edges and angles around the shape, remembering that a flip reverses the order.
Shape Matching
Shape Matching: Jagged Outlines
Pupils match jagged shapes built from unit squares by comparing their complete outlines under turns and flips, using the order of steps and notches around the edge.
Shape Matching
Shape Matching: Square-Built Shapes
Pupils find the shape made of six to eight unit squares that matches the target after turning or flipping, without resizing, using distinctive features to compare.
Similar Triangles
Similar Triangles: Counting Region by Region
Pupils read each divided triangle in the order bottom-left, bottom-centre, bottom-right, then top, see that each region adds one symbol, and apply the same count rule to the second triangle.
Similar Triangles
Similar Triangles: Shading and Dot Cycles
Pupils find how shading and the number of small dots cycle from region to region in the first triangle, then apply the same cycles in the second triangle to fill the gap.
Similar Triangles
Similar Triangles: Three Changes at Once
Pupils identify three features that change from region to region, from direction, marker position, shading and dot count, and apply all three changes to fill the gap in the second triangle.
Similar Triangles
Similar Triangles: Turns and Moving Markers
Pupils find how the direction turns and the perimeter marker moves from region to region in the first triangle, then apply the same changes in the second triangle to fill the gap.
Star Matrices
Star Matrices: Matching Counts Across the Centre
Pupils find that each inner triangle contains as many squares as there are symbols in the outer triangle directly opposite it, and use this to fill the missing inner region.
Star Matrices
Star Matrices: Shading and Dots Across the Centre
Pupils find how shading and the number of small dots change from each outer region to the inner region opposite it, and apply the same changes to fill the missing inner region.
Star Matrices
Star Matrices: Three Changes Across the Centre
Pupils identify three features that change from each outer region to the inner region opposite it, from direction, marker position, shading and dot count, and apply all three to fill the missing inner region.
Star Matrices
Star Matrices: Turns and Markers Across the Centre
Pupils pair each outer region with the inner region directly opposite it, find how the direction turns and the perimeter marker moves between them, and apply the same changes to fill the missing inner region.
Triangle Series: Two Streams
Two Streams: Shading and Dot Cycles
Pupils follow a shading cycle and a dot-count cycle through the upright triangles only, ignoring the inverted stream, to complete the upright sequence.
Triangle Series: Two Streams
Two Streams: Three Changes at Once
Pupils identify three features changing through the upright triangles, from direction, marker position, shading and dot count, and complete the upright sequence while ignoring the inverted stream.
Triangle Series: Two Streams
Two Streams: Turning in Opposite Directions
Pupils find that symbols in upright triangles turn 90 degrees clockwise while inverted triangles hold solid symbols turning anticlockwise, and fill the missing upright triangle without falling for inverted-stream traps.
Triangle Series: Two Streams
Two Streams: Turns and Moving Markers
Pupils separate the upright triangles from the inverted ones and continue the upright sequence, where the direction turns a quarter-turn and the perimeter marker moves one side.
Vertical Codes: Shapes to Letters
Vertical Codes: Direction and Marker Position
Pupils crack a two-letter code in which the first letter records direction and the second records marker position, comparing references that differ in only one feature.
Vertical Codes: Shapes to Letters
Vertical Codes: Shading and Dot Count
Pupils crack a two-letter code in which the first letter records shading and the second records the number of small dots, and build the code for the test figure.
Vertical Codes: Shapes to Letters
Vertical Codes: Shape and Fill
Pupils work out a two-letter code in which the first letter records shape and the second records fill, using references laid out vertically, and build the code for the test figure.
Vertical Codes: Shapes to Letters
Vertical Codes: Three Features
Pupils crack three-letter codes in which each position records one of direction, marker position, shading or dot count in an order that changes from puzzle to puzzle, and build the test code.