DiscoNumbers

What you see

Every trial runs in three phases: watch, reproduce and compute. Before you press Start, the prompt above the board names the question you will be asked, or says that it comes later. While you watch and reproduce, a line under the board repeats the question.

1. Watch. You press Start (or Space). After a 300 ms pause, pads light one at a time. Each pad carries a single digit, and every digit on the floor stays visible while the route runs. At per-step levels the lit pad also shows its sign in front of its value, for example −7. A row of numbered step markers under the pads shows how far through the route you are. There is no gap between flashes: each step lasts exactly the step time for your level (600 ms at the start, 400 ms at the top).
2. Reproduce. The flashing stops and you select the pads in the order they lit. The digits are still printed on the pads in this phase. Each selected pad gets a small order badge. You cannot select the same pad twice in a row (the route never does that either). Undo removes your last selection, and Finish ends the phase early. When you have selected as many pads as there were steps, the trial moves on by itself.
3. Compute. The floor is hidden, an expression strip appears (for example ? + ? − ? + ? =), and you type the result on a keypad that includes a minus key for negative answers. Answers have at most three characters. Press Check answer or Enter to submit. After the check the floor returns with its values, each step marker turns green or red for the pad you selected there, and the expression strip shows the real values and the result.

In the compute phase the floor is hidden, so the values must come from memory. The route above was 9, 2, 3, 7, so the total is 21.

How the ten levels differ

Our version starts every practice session at level 3 and moves you one level at a time. The level sets six things at once:

The three questions:

• Total: add every value on the route.
• Alternating: first + second − third + fourth − fifth, and so on. The expression strip in the compute phase spells the signs out for you.
• Per-step signs: each flash after the first carries its own + or − with it. Those signs are shown only while the route runs; the compute strip shows each one as ±, so you must remember them.

A few generator rules are worth knowing. Two pads can carry the same digit. A route never lights the same pad twice in a row, and from level 8 at most one pad appears twice in the route. The generator also rejects routes whose running result would go above 99 or below −20 at any step, so a sensible answer is always a small number.

What it measures

DiscoNumbers feeds the Working under load facet of Memory, which it shares with GridRecall, and it carries 14 per cent of the Memory dimension. The skill is working memory in its narrower, research sense: not only holding information but keeping it available while you do something else with it. Wilhelm, Hildebrandt and Oberauer describe working memory capacity as the ability to build, maintain and update arbitrary bindings, such as items bound to list positions. Here each value is bound to a place on the floor and to a position in the route.

The task borrows from three research families.

• Spatial sequence span. Reproducing a lit route is the Corsi block-tapping task in modern dress: blocks are tapped in order and you copy the order. Kessels and colleagues standardised its administration and scoring as a measure of visuospatial short-term memory.
• Complex span. Operation span and reading span interleave a processing job with a storage job. These tasks predict comprehension and reasoning better than simple span does.
• Memory updating. In the updating paradigm, first built by Salthouse and colleagues and adapted for testing by Oberauer and colleagues, you hold a few values and then change them with arithmetic. DiscoNumbers' per-step levels sit closest to this family.

Why two jobs and not one? Baddeley's multi-component model separates a visuospatial store, a speech-based phonological loop and an executive that coordinates them. Two findings from that tradition shape the method later in this lesson. First, Cocchini and colleagues found that holding a verbal memory load and a visual memory load at the same time caused little mutual interference. A route (where) and a set of numbers (what) can share your mind better than two lists of numbers could. Second, Fürst and Hitch showed that mental addition leans on the phonological loop to hold the problem. When the numbers stayed visible during calculation, blocking that store had no effect. In DiscoNumbers the digits stay visible while you reproduce, and that is the moment to calculate.

How it is scored here

Each trial is scored out of 10,000 points in two parts that are kept separate on purpose:

• Sequence credit, up to 6,000. We take the longest run of your selections that appears in the true route in the same order (the longest common subsequence). 6,000 × (that run ÷ route length). A single swapped pair costs one step of credit, not the whole sequence.
• Answer credit, 4,000. Your number must equal the true answer computed on the real route, not on the route you selected.
• Correct (10,000) needs both an exact reproduction and the right answer. Anything else with some credit is Partly correct; zero credit is Incorrect.

Two consequences follow directly from the rules.

• Always finish the route. Adding a selection can never shorten the longest in-order run, so a guessed final selection can only help. Pressing Finish early throws away free chances.
• The answer is checked against the truth. If you select a wrong pad and then compute from the pads you selected, you lose both parts. Your session report tracks this as Memory slips that cost the answer.

Levels. Practice uses a simple staircase: a Correct trial moves you up one level, a Partly correct trial keeps you where you are, and an Incorrect or skipped trial moves you down one. Because almost any attempt earns some sequence credit, you rarely drop; you climb only on perfect trials.

The 0–100 score. Time is not part of your DiscoNumbers score; only accuracy counts, weighed against how hard the trial was. The measured difficulty rises with route length and with faster flashing. On our scale, 50 means you scored what the difficulty you work at predicts; above 50 means you beat that expectation. Feedback after each trial reads like: “5 of 6 pads in the right order; the result is 14.”

Where you will meet it

No vendor task we could verify is a copy of DiscoNumbers. Its two halves, holding a spatial sequence and doing mental arithmetic under pressure, both appear in real selection tests.

The method

1. Read the question before you press Start

   At levels 1 to 6 and 9 to 10 the question type is named in the prompt before you press Start. Decide now: running total, pairs for alternating, or signs to memorise.

2. Watch the route as a shape

   Do not name pad positions. Let your eyes trace the path and store it as a gesture: “up, across, down-left”. This keeps the route in spatial memory and leaves your inner voice free for numbers.

3. Keep one number in your inner voice

   If the pace allows (600 ms is enough for most people at levels 1 to 4), keep a silent running total while watching. One number is far lighter to hold than a list of five.

4. At per-step levels, store the signs as a rhythm

   Per-step signs vanish after the watch phase. Chunk them in threes, for example “plus minus minus, plus plus minus”. The values you can read again later; the signs you cannot.

5. Select and compute together

   During reproduction the digits are back on the pads. As you select each pad, read its value and update your total. Your watch-phase total, if you kept one, becomes a check.

6. Never stop short, then type and check the sign

   Select all the steps even if the last one is a guess. Then enter the answer, including the minus key when the result is negative, and submit.

Worked example 1: alternating at level 5

The shape is “skip along the top, drop back left, run right along the bottom”. What do you type?

Show the solution

Use the pairs trick. Alternating always starts with the first value, then adds the difference of each following pair: first + (second − third) + (fourth − fifth).

• First value: 7.
• Pair one: 4 − 9 = −5, running result 2.
• Pair two: 2 − 6 = −4, running result −2.

Type −2, using the minus key. Pairs turn five items into three small numbers, and each pair is a single subtraction you do as you select.

Worked example 2: per-step signs at level 9

Try this one live. The flashes below run at 450 ms each, the level 9 pace. The first value has no sign; every later value carries its own.

Ordering exerciseSign in to try it

Show the solution

Running result: 8, then 11, 5, 3, 8, 12, and finally 3.

The sign rhythm was “plus minus minus, plus plus minus”. In the real game you would store that rhythm and the route during the watch phase. Then, during reproduction, you would read each value off the pad you select and apply the next sign. You do not need to have caught every value in the flashes, because the pads show them again. You do need every sign, because nothing shows them again.

Worked example 3: the question arrives late at level 7

At levels 7 and 8 the prompt says only that the question comes later. Suppose the six values on your route are 5, 8, 3, 9, 1, 6.

Show the solution

Keep the values in pairs as you select: 5, then (8, 3), (9, 1), and the lone 6. From that one memory you can produce either answer quickly.

• Alternating: 5 + (8 − 3) + (9 − 1) + 6 = 5 + 5 + 8 + 6 = 24.
• Total: 5 + 8 + 3 + 9 + 1 + 6 = 32.

In the current version the withheld question at levels 7 and 8 is always the alternating one. Prepare for it, but hold the pairs so you are not caught out if that ever changes.

Tips and traps

Levelling up

What changes as you climb, and how to adapt:

• Levels 1 to 4 (totals). Build the running-total habit here while the pace is gentle. Aim to finish every watch phase already knowing the answer.
• Levels 5 and 6 (alternating). Switch to pairs. The step time drops to 500 ms at level 6, so the reproduce phase becomes your main calculation time.
• Levels 7 and 8 (question after recall). Hold values as pairs. The board grows to ten pads and one repeat is allowed, so the route shape matters more than ever.
• Levels 9 and 10 (per-step). The load is now route plus sign rhythm plus arithmetic, at 450 ms and then 400 ms per step with up to eight steps on twelve pads. Put the route and the signs first; the values will be on the pads when you select.

Research on working memory training is clear about limits. In a meta-analysis of 87 publications, Melby-Lervåg, Redick and Hulme found that training improved performance on similar memory tasks but produced no reliable far transfer to reasoning, reading or arithmetic. Expect this practice to make you better at this family of tests, which is the point before a placement round. Do not expect it to raise your general intelligence.

1. Week 1
   • Three sessions of 10 minutes at the starting level
   • Say the running total silently on every trial, even when it feels unnecessary
   • Finish every route; never press Finish early
2. Week 2
   • Three sessions aiming to hold level 5 to 6
   • Use the pairs trick for every alternating question
   • After each session, check the ‘Memory slips that cost the answer’ reading in your report
3. Week 3
   • Two sessions pushing into levels 7 to 9
   • Practise chunking sign rhythms in threes
   • One session of GridRecall for the same facet with a different secondary task
4. Week before the test
   • Short daily sessions of 5 to 8 minutes, no new strategies
   • Warm up with two or three trials before any timed practice test

Check yourself

5 practice questions

1. An alternating trial’s route values are 6, 3, 8, 2, 5. What is the answer?
2. You reproduce a six-step route exactly but type the wrong answer. What does the trial score, and what happens to your level?
3. You are unsure of the last two steps of a seven-step route. What should you do?

and 2 more

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Sources

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2. Aon. Prepare for your online assessment (gridChallenge, digitChallenge descriptions). aon.com
3. Baddeley, A. (2003). Working memory: Looking back and looking forward. Nature Reviews Neuroscience, 4, 829–839. doi:10.1038/nrn1201
4. Cocchini, G., Logie, R. H., Della Sala, S., MacPherson, S. E., and Baddeley, A. D. (2002). Concurrent performance of two memory tasks: Evidence for domain-specific working memory systems. Memory and Cognition, 30(7), 1086–1095. doi:10.3758/bf03194326
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8. Fürst, A. J., and Hitch, G. J. (2000). Separate roles for executive and phonological components of working memory in mental arithmetic. Memory and Cognition, 28(5), 774–782. doi:10.3758/bf03198412
9. Kessels, R. P. C., van Zandvoort, M. J. E., Postma, A., Kappelle, L. J., and de Haan, E. H. F. (2000). The Corsi Block-Tapping Task: Standardization and normative data. Applied Neuropsychology, 7(4), 252–258. doi:10.1207/S15324826AN0704_8
10. 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
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14. HireVue. Game-based cognitive ability assessment explained. hirevue.com
15. Candidate-reported formats: PrepInsta, Capgemini game-based aptitude (link) and Cognizant GenC game-based questions (link); GraduatesFirst, Arctic Shores guide (link).

Put it into practice: DiscoNumbersSign in to try it