Puzzle Reconstruction

What you see

Each tile combines four features, and every tile on a board is unique:

• a glyph: circle, square, triangle, diamond, star or hexagon;
• a fill: outline, striped or solid;
• a hue band: a coloured bar across the top, from a palette of three to eight bands depending on the level;
• a corner mark: a small dark square in one of the four corners. It exists so that no tile depends on colour vision alone.

A trial has up to three phases.

1. Study. The start screen reads “Memorise the grid, then rebuild it.” You press Start (or Space), a 3-2-1 countdown runs, and the trial clock starts when it ends. The grid then appears under the prompt “Memorise the grid.” with a countdown bar labelled Study.
2. Pause. At levels 6, 8, 9 and 10 the grid is replaced by a blank panel, the prompt reads “Keep the grid in mind.”, and a second countdown bar, labelled Pause, runs for 5 to 10 seconds.
3. Rebuild. The prompt reads “Rebuild the grid.” An empty grid, labelled Grid, appears with the Tray beside it on a wide screen or below it on a phone; the tray has as many columns as the grid. Select a tray tile to pick it up, then select an empty cell to drop it. Select a placed tile to send it back to the tray. Escape puts a held tile down, and the arrow keys move between cells. The line under the board counts your progress, for example “5 of 16 cells filled.”, and reads “All 16 cells filled.” once the grid is full. You then submit with Check answer or Enter. You cannot submit a half-empty grid.

The tray is shuffled so that it never hands you the answer in order. There is no per-trial deadline in the rebuild phase; the practice timer only records how long you took.

How the ten levels differ

Sessions start at level 3. The level changes five settings: grid size, palette width, how different tiles must be from each other, study time and pause time.

The fourth column matters more than it looks. Up to level 5, any two tiles differ in at least two features, so a glance usually separates them. From level 6 two tiles may differ in only one feature, for example two solid stars with the same band whose corner marks sit in different corners. The narrowing palette makes colour less useful as the levels rise; at level 10 only three bands exist for 25 tiles.

What it measures

Puzzle Reconstruction is the only game in the Visual memory facet of Memory, where it carries 14 per cent of the dimension. It also contributes 10 per cent of the Spatial dimension through the Spatial construction facet. The two labels describe the two halves of the trial: taking in a static visual pattern, and assembling it again from parts.

Visual rather than sequential memory. Della Sala, Gray, Baddeley and colleagues built the Visual Patterns Test to measure short-term visual memory largely shorn of its spatial and sequential part. People see a grid pattern and reproduce it. Comparing it with the Corsi block task, where you copy a sequence of taps, they found evidence that the two are separable: some patients were impaired on one and not the other, and different distracting tasks disrupted each. Puzzle Reconstruction belongs to the pattern family. Its memory cousins DiscoNumbers and GridRecall belong to the sequential one.

Object-location binding. Postma, Kessels and van Asselen split remembering where things are into three processes: processing the object, processing the location, and binding the two together. The tray removes most of the first job, because every tile is visible when you rebuild. What is left is the binding: this tile, that cell. Wilhelm, Hildebrandt and Oberauer put exactly this kind of binding, objects bound to spatial locations, at the centre of their definition of working memory capacity.

Spatial construction. Assembling a design from separate pieces is the idea behind Kohs's block-design tests, published in 1920. Our game adds a memory demand on top: the model disappears before you start building, so you construct from memory rather than by copying.

Those numbers explain the design. Nine to 25 tiles far exceed three or four objects, so raw visual capacity cannot carry you. With 7 to 10 seconds of study you can look several times, group and name what you see, and rehearse it. The game therefore rewards strategy layered on top of visual memory.

How it is scored here

Every cell of your rebuilt grid is judged against the original:

• Exact: the right tile in the right cell. Full credit.
• Adjacent: the tile sits one cell up, down, left or right of its home. Half credit. Diagonal does not count.
• Wrong: anywhere else. No credit.

The trial score out of 10,000 blends two parts. 80 per cent is placement: (exact + half the adjacent) ÷ number of tiles. 20 per cent is structure: of all pairs of tiles that shared a row or a column in the original, the share that still appear in the same reading order (left to right, top to bottom). Structure rewards keeping the overall layout even when individual tiles drift.

Only a rebuild with every tile exact counts as Correct and earns 10,000. Anything else with some credit is Partly correct. After you check, each cell is marked: green for the right cell, amber for one cell off (directly above, below or beside its home) and red for further away. A line sums it up, for example “7 of 9 tiles in the right cell; 2 one cell off”.

Levels. Practice moves you up one level after a perfect rebuild, keeps you in place after a Partly correct one, and moves you down after a skipped trial. Near misses therefore do not cost you your level, but they do not lift you either: only a perfect grid does.

The 0–100 score. Time is not part of your score for this game. Your accuracy is compared with what the difficulty you work at predicts, where the measured difficulty grows with the number of tiles and with shorter study times. 50 means you matched that prediction. Because harder boards predict lower accuracy, 85 per cent on a 5 × 5 board can count for as much as a perfect 3 × 3. Your session report shows Pieces placed exactly, Layout preserved and Pieces one cell out. A high Pieces one cell out count means your map was nearly right and your precision needs work.

Where you will meet it

A tile-for-tile copy of this game is rare in hiring tests. Its two ingredients, remembering a briefly shown pattern and remembering where things were in a grid, are common.

The method

1. Know the level before you start

   The level table above gives the study time and whether a pause follows. Decide your plan before you press Start: a 3 × 3 with 10 seconds calls for a different approach from a 5 × 5 with 8 seconds and a pause.

2. Spend the first second on a survey, not a tile

   Glance over the whole grid. Which glyphs appear twice or more? Which tile is the only one of its kind? Repeats are where mistakes happen, so they get your attention.

3. Name each row with the cheapest label that works

   Say glyphs row by row: “star, circle, square”. Add the fill only where a glyph repeats (“solid star … outline star”). Add a band colour or corner mark only where glyph and fill both repeat. The tray will show you the full tile later; your label only has to point to it.

4. Anchor the corners and the loners

   Corner cells and one-of-a-kind tiles are easy to place and give you fixed points to build around.

5. During a pause, walk the grid

   Rehearse by moving your attention across the empty panel cell by cell and repeating the row labels. Awh, Jonides and Reuter-Lorenz showed that spatial memories are kept alive by shifting attention to the remembered locations, and that stopping people from doing so harmed recall.

6. Rebuild from certainty outwards, and fill every cell

   Place anchors first, then complete rows. For the last few tiles, use elimination: only certain tiles remain and only certain cells are empty. If you are unsure, put a tile where you think it lived or next to it. One cell off still earns half credit.

Worked example 1: the least you need to remember

You have ten seconds. What is the shortest code that lets you rebuild this grid perfectly from the tray?

Show the solution

Start with glyphs only, row by row:

• Row 1: star, circle, square
• Row 2: triangle, diamond, star
• Row 3: hexagon, circle, triangle

Three glyphs repeat: star, circle and triangle. For each, one extra word is enough. The solid star is top left and the outline star is on the right of row 2. The outline circle is at the top and the solid circle at the bottom. The outline triangle is on the left of row 2 and the striped triangle at bottom right.

That is nine short words plus three fill words. You never needed the hue bands or the corner marks, because at this level the tiles differ in at least two features. Saying “star, circle, square” three times during the study period is realistic in ten seconds. Trying to store every feature of every tile is not.

Worked example 2: when tiles differ by one feature

These four tiles sit in a 2 × 2 block of a level 8 board. How should you encode them?

Show the solution

Name the shared part once and then only the differences. The block is “stars, mostly solid, mostly the same”. Now tag each cell with what makes it different:

• Top left: the plain one (mark top left, first band colour, solid).
• Top right: mark bottom right.
• Bottom left: different band colour.
• Bottom right: striped.

In the tray you will see four stars. Place the three with a distinctive feature by their tags, and the plain one goes in the remaining cell. This is the “objects, not features” idea from Vogel and colleagues used deliberately: you hold one group object plus three small exceptions instead of sixteen separate features.

Worked example 3: two tiles you are unsure about

Late in a 3 × 3 rebuild, seven tiles are certain. Two remain: a hexagon and a diamond. You know they belonged to the two cells in the top-left corner, side by side, but not which way round.

Show the solution

Place them and move on. If you are right you score 10,000. If you are wrong, both tiles are one cell from home, so they earn half credit each, and almost every row and column pair keeps its order. The trial scores 9,000, the first case in the scoring figure. A guess between two neighbouring cells costs at most 1,000 points. The expensive errors are tiles placed far from home and whole rows reversed.

Tips and traps

Levelling up

• Levels 1 and 2 (3 × 3). Build the survey–name–anchor routine until it is automatic. Aim for perfect grids; you climb only on perfect trials.
• Levels 3 to 5 (4 × 4). Sixteen tiles take longer to name. Name in rows of four, and use the pause between rows to glance back at the first row once. Study time drops to 7 seconds at level 5.
• Level 6. The first pause, and the first boards where tiles may differ in one feature. Rehearse by walking the grid during the pause.
• Levels 7 to 10 (5 × 5). You cannot name 25 tiles in 8 to 10 seconds. Name the corners, the loners and the look-alike clusters. Rebuild the rest by elimination and by the layout you remember. Pauses reach 10 seconds at level 9.

As with all memory practice, gains are largest on tasks like the one you practise. Meta-analyses of working memory training find reliable improvement on similar memory tasks but no convincing far transfer to broader abilities. This game makes you better at pattern-memory tasks; it will not change your general intelligence.

1. Week 1
   • Three 10-minute sessions from the starting level
   • On every trial, say the row labels aloud or under your breath
   • Check ‘Pieces one cell out’ in your report after each session
2. Week 2
   • Three sessions aiming to hold 4 × 4 boards perfectly
   • Practise anchoring corners before naming rows
   • Start using the half-credit rule: never hesitate over two neighbouring cells
3. Week 3
   • Two sessions reaching into levels 6 to 8
   • Rehearse by walking the grid during every pause
   • One GridRecall session for location memory under interruption
4. Week before the test
   • Short daily sessions, same routine every time
   • Two warm-up trials before any timed practice test

Check yourself

5 practice questions

1. In a 3 × 3 rebuild everything is perfect except two tiles in side-by-side cells, which are swapped. What does the trial score?
2. Why does a rebuild with every row mirrored score so poorly?
3. A 5 × 5 board has 25 tiles, and there are 18 possible glyph-and-fill pairs. At least how many tiles must repeat a glyph-and-fill pair already used on the board?

and 2 more

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Sources

1. Awh, E., Jonides, J., and Reuter-Lorenz, P. A. (1998). Rehearsal in spatial working memory. Journal of Experimental Psychology: Human Perception and Performance, 24(3), 780–790. doi:10.1037/0096-1523.24.3.780
2. Brown, L. A., Forbes, D., and McConnell, J. (2006). Limiting the use of verbal coding in the Visual Patterns Test. Quarterly Journal of Experimental Psychology, 59(7), 1169–1176. doi:10.1080/17470210600665954
3. Cowan, N. (2001). The magical number 4 in short-term memory: A reconsideration of mental storage capacity. Behavioral and Brain Sciences, 24(1), 87–114. doi:10.1017/S0140525X01003922
4. Della Sala, S., Gray, C., Baddeley, A., Allamano, N., and Wilson, L. (1999). Pattern span: A tool for unwelding visuo-spatial memory. Neuropsychologia, 37(10), 1189–1199. doi:10.1016/S0028-3932(98)00159-6
5. Kohs, S. C. (1920). The block-design tests. Journal of Experimental Psychology, 3(5), 357–376. doi:10.1037/h0074466
6. Melby-Lervåg, M., Redick, T. S., and Hulme, C. (2016). Working memory training does not improve performance on measures of intelligence or other measures of far transfer. Perspectives on Psychological Science, 11(4), 512–534. doi:10.1177/1745691616635612
7. Postma, A., Kessels, R. P. C., and van Asselen, M. (2008). How the brain remembers and forgets where things are: The neurocognition of object-location memory. Neuroscience and Biobehavioral Reviews, 32(8), 1339–1345. doi:10.1016/j.neubiorev.2008.05.001
8. Vogel, E. K., Woodman, G. F., and Luck, S. J. (2001). Storage of features, conjunctions and objects in visual working memory. Journal of Experimental Psychology: Human Perception and Performance, 27(1), 92–114. doi:10.1037/0096-1523.27.1.92
9. Wilhelm, O., Hildebrandt, A., and Oberauer, K. (2013). What is working memory capacity, and how can we measure it? Frontiers in Psychology, 4, 433. doi:10.3389/fpsyg.2013.00433
10. Aon. Prepare for your online assessment (gridChallenge). aon.com
11. HireVue. Game-based cognitive ability assessment explained. hirevue.com
12. Candidate-reported formats: PrepInsta, Cognizant GenC game-based questions (link) and Capgemini game-based aptitude (link).

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