Sequence Transformer

What you see

The screen is a vertical pipeline, read from top to bottom:

• Input: a row of four to six distinct symbols (circle, square, triangle, diamond, star, hexagon), with its positions numbered 1, 2, 3… across the top.
• Operators: one to three bands of wires, numbered down the left. Each wire carries the symbol at one position of the row above to a position of the row below; the small dots between bands stand for the row in between.
• Output: at the bottom, with its positions numbered underneath. When you predict the output it shows empty slots. When one operator is hidden, the output shows the target row, and the hidden operator is a dashed band with a ?.

Below the pipeline are three to six numbered options: whole output rows when you predict the output, or small wire diagrams when an operator is hidden. When you choose an option it appears in the pipeline, in the output row or the hidden band, so you can see it in place. Press an option's number or click it to choose, then Check answer or Enter. There is no countdown; a practice timer records how long you take.

How to read one operator

This is the rule that everything else rests on. Follow each wire upwards from an output position to the input position it comes from. In this lesson we write an operator as a code that lists, for each output position in turn, the input position it takes: 3·1·4·2 means position 1 takes item 3, position 2 takes item 1, position 3 takes item 4 and position 4 takes item 2. On the board that is four wires: from input 3 down to position 1, from input 1 to position 2, from input 4 to position 3 and from input 2 to position 4.

A few codes are worth recognising at sight:

• A digit equal to its own position (a 3 in third place) means that symbol stays put.
• Two positions that name each other (2·1·…) are a swap.
• A descending code (4·3·2·1) reverses the row.
• 2·3·4·1 moves everything one place left and wraps the first symbol to the end. 4·1·2·3 moves everything one place right.

In a pipeline, each operator acts on the row produced by the one above it.

How the ten levels differ

Sessions start at level 3 and move one level at a time.

No operator is ever the identity (a code that changes nothing), and the input row is always shuffled, so the input itself never gives the code away.

The wrong options are built to be near misses. In predict trials, most wrong rows are the right row with two symbols swapped; from level 6 one is a less similar rearrangement. In find trials, most wrong codes are the right code with two entries swapped. From level 7 one wrong code is usually the reverse-direction reading of the right one, and at level 10 another is usually the right code shifted by one place. Because every symbol in a row is distinct, exactly one option can work.

What it measures

Sequence Transformer is the smallest contributor to the Memory dimension (8 per cent) and also feeds Pattern recognition in Reasoning (6 per cent). It sits between the two because it asks you to do reasoning inside working memory: apply a rule to a sequence, keep the result, apply the next rule to that.

Manipulating order, not just storing it. Reciting digits backwards or rearranging a list is harder than repeating it. Kessels and colleagues found that backward digit span was harder than forward span, and suggested the backward version also calls on the executive part of working memory. Letter–Number Sequencing, a Wechsler subtest, asks people to reorder a mixed list. Crowe found that much of its variance is shared with digit span forward and backward, with extra contributions from processing speed and visuospatial working memory. Each operator here is a small reordering job of that kind.

Storage during processing, and relational integration. Lewandowsky, Oberauer and colleagues built their working memory battery around two functions: storage in the context of processing, and relational integration, meaning combining several elements into one structure. A multi-step pipeline needs both. You store an intermediate row while you read the next code, and every code is a set of position-to-position relations applied together.

Relational complexity. Halford and colleagues showed that performance drops sharply when a problem requires more than about four variables to be considered at once. A six-symbol code taken whole exceeds that. Taken one position at a time, it is a single link. The method below is built on that idea.

How it is scored here

Each trial is simply right or wrong: 10,000 points for the correct option, 0 for any other. There is no partial credit, because every wrong option is a complete wrong answer.

• Levels. A correct answer moves you up one level; a wrong or skipped one moves you down one. Expect to move almost every trial, settling around the level where you are right about half the time.
• Speed. Unlike the other memory games, time counts a little here. Accuracy carries most of the weight (about 85 per cent in the formula) and speed the rest. A very slow correct answer is worth a little less than a quick correct one; a fast wrong answer is still worth nothing. Never trade accuracy for speed.
• The 0–100 score. 50 means you matched what the difficulty you work at predicts. Above 50 means you beat it.

Where you will meet it

This is the game in our library with the clearest real-world twin. Aon's switchChallenge shows a row of shapes, a code and a resulting row, and asks you to find the code. Its instructions use the same reading as ours. In one of Aon's own worked solutions, the last shape moves to the front of the output, “so the code has to start with 4-”: position 1 takes item 4. Our SwapCode lesson covers a related permutation game in the Reasoning path.

In more difficult questions, the numerical codes may be presented across multiple rows. In those cases, the output of the first code is the input for the next code.

The method

1. Read the question

   Which row do the operators produce? or Which option is the hidden operator? The two need different moves, so decide before you start computing.

2. Read every code as ‘position takes item’

   Say it to yourself once: “1 takes 3, 2 takes 1…”. Mark fixed points, swaps and reversals first; they cost nothing to apply.

3. Predict: trace one slot backwards

   To find what lands in output position 1, read the last code's first digit, say 5. Go to the code above and read its 5th digit, say 4. That points to input item 4. You carry one number, not a whole row. The digits chain like this because each operator takes its input from the row above.

4. Predict: let the options tell you which slots to trace

   Most wrong options differ from the right one in only two positions. Trace one slot and cross out every option that disagrees. Then trace another. Usually two or three slots settle it.

5. Find: build the rows either side of the gap

   Push the input forward through every visible code above the gap. Undo every code below the gap, working up from the target. To undo a code, read it the other way: item k goes back to the position given by the k-th digit. Now you have the row entering the hidden slot and the row leaving it.

6. Find: read the hidden code off, then check it

   For each position of the leaving row, find where that symbol sits in the entering row; that position is the digit. Before submitting, check one or two digits against the options. From level 7 the reverse-direction reading is usually waiting among the options.

Worked example 1: one code at level 1

Input ○ □ △ ◇ goes through 3·1·4·2. What comes out?

○□△◇????

Show the solution

Position 1 takes item 3 (△). Position 2 takes item 1 (○). Position 3 takes item 4 (◇). Position 4 takes item 2 (□). The output is △ ○ ◇ □, the left-hand result in the pull and push figure further down this page.

Worked example 2: two codes at level 4

Show the solution

Trace slots backwards instead of building both rows.

• Output position 1. Operator 2's first digit is 5. Operator 1's fifth digit is 4. Input item 4 is ◇. Option 1 starts with □, so 1 is out.
• Output position 2. Operator 2's second digit is 4. Operator 1's fourth digit is 5. Input item 5 is ★. Option 3 has △ there, so 3 is out.
• Output position 3. Operator 2's third digit is 3. Operator 1's third digit is 3. Input item 3 is △. Option 4 has ○ there, so 4 is out.

The answer is option 2: ◇ ★ △ ○ □. You traced three slots and never held a full intermediate row. As a check, operator 1 swaps the first two and the last two symbols (□ ○ △ ★ ◇), and operator 2 reverses that row, which gives option 2.

Worked example 3: a hidden second code at level 5

Show the solution

Operator 1 is 4·3·2·1, a reversal, so the row entering the gap is ◇ △ □ ○. The row leaving it is the target, △ ○ ◇ □. Now read the hidden code position by position:

• Output position 1 is △, which sits at position 2 of the entering row, so the code starts with 2.
• ○ sits at position 4, so the next digit is 4.
• ◇ sits at position 1, then 1.
• □ sits at position 3, then 3.

The hidden code is option 2: 2·4·1·3. Option 1, 3·1·4·2, is the trap: it is what you get if you read the mapping in the wrong direction (“item 1 goes to position 2…”). Options 3 and 4 are the right code with two digits swapped.

Worked example 4: the hidden first code at level 10

At level 10 the hidden slot is always first, so you must work backwards from the target.

Input ○ □ △ ◇, a hidden first code, then 2·3·4·1, and the target ○ ◇ □ △. What is the hidden code?

Show the solution

Undo operator 2. 2·3·4·1 says position 1 took item 2, position 2 took item 3, and so on. Going backwards, each target symbol returns to the position its digit names: ○ goes to position 2, ◇ to 3, □ to 4 and △ to 1. The row in between is △ ○ ◇ □.

Read the hidden code. △ is input item 3, ○ is item 1, ◇ is item 4, □ is item 2. The hidden code is 3·1·4·2. At level 10, expect its reverse-direction reading (2·4·1·3) and a one-place shift among the six options.

Tips and traps

Levelling up

• Levels 1 to 3. One code. Drill the reading until it is automatic, and learn to recognise swaps, reversals and shifts at a glance.
• Levels 4 and 6. Two codes. Switch to backward slot-tracing and option elimination.
• Levels 5 and 7. Find the operator. Practise undoing codes; it is the same skill in reverse.
• Levels 8 and 9. Three codes on six symbols. Trace slots rather than rows. For find trials with the gap in the middle, build the row above the gap forwards and the row below it backwards.
• Level 10. Hidden first code, six options including the reverse-direction reading and a one-place shift. Undo carefully and verify two digits before you submit.

Because the level moves after every trial, a session naturally settles where you are right about half the time. That is where learning happens, so do not be discouraged by the frequent drops.

1. Week 1
   • Three 10-minute sessions from the starting level
   • Say ‘position takes item’ for every code until you no longer need to
   • Note every error: was it direction, order of codes, or a slip?
2. Week 2
   • Three sessions aiming to hold levels 5 to 6
   • Use backward slot-tracing on every predict trial
   • Undo codes out loud on every find trial
3. Week 3
   • Two sessions pushing into levels 8 to 10
   • Before each submission, verify one extra digit
   • One SwapCode session for a related permutation format
4. Week before the test
   • Short daily sessions focused on speed with accuracy
   • If you face Aon’s switchChallenge, practise its 4-digit format with a timer

Check yourself

6 practice questions

1. Input ○ □ △ ◇ goes through the code 2·4·1·3. What is the output?
2. In a six-symbol code, the fourth digit is 4. What does that tell you?
3. Input A B C D becomes D A B C. Which code did it?

and 3 more

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Sources

1. Aon. Practice tasks: Deductive logical reasoning (switchChallenge). PDF
2. Aon. Prepare for your online assessment. aon.com
3. Crowe, S. F. (2000). Does the letter number sequencing task measure anything more than digit span? Assessment, 7(2), 113–117. doi:10.1177/107319110000700202
4. Halford, G. S., Baker, R., McCredden, J. E., and Bain, J. D. (2005). How many variables can humans process? Psychological Science, 16(1), 70–76. doi:10.1111/j.0956-7976.2005.00782.x
5. Kessels, R. P. C., van den Berg, E., Ruis, C., and Brands, A. M. A. (2008). The backward span of the Corsi Block-Tapping Task and its association with the WAIS-III Digit Span. Assessment, 15(4), 426–434. doi:10.1177/1073191108315611
6. Lewandowsky, S., Oberauer, K., Yang, L.-X., and Ecker, U. K. H. (2010). A working memory test battery for MATLAB. Behavior Research Methods, 42(2), 571–585. doi:10.3758/BRM.42.2.571
7. Candidate-reported formats: PrepInsta, Capgemini game-based aptitude (link) and Cognizant GenC game-based questions (link).

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