Training your look-ahead

What practice does, and what it does not

The brain-training literature is clear on the broad pattern. A major review of the studies cited by brain-training companies found extensive evidence that training improves performance on the trained tasks, less evidence for closely related tasks, and little evidence for distantly related tasks or everyday cognition. Meta-analyses of chess, music and working-memory training reach a similar verdict: the apparent benefits shrink as study quality improves, and far transfer "rarely occurs". Diamond's review of executive-function training notes that transfer from computerised working-memory or reasoning training has been narrow.

So practising Towers of London will not make you a better project manager by itself. What practice does reliably change is performance on the task family you practise:

• Strategy discovery. Executive tasks are prone to sudden jumps when someone finds a better approach, which is one reason their test-retest reliability tends to be low. On the Tower of London, naive participants started with systematic exploration, much like a search algorithm, and, with practice, developed markedly more efficient strategies within the session.
• Format familiarity. Knowing the controls, the move budget and how scoring works removes the first-attempt penalty that has nothing to do with your ability.

That makes targeted practice legitimate preparation for a game-based assessment in the same family. It also tells you what to practise: strategies that carry across puzzles, not one puzzle's answers.

Seven strategies that carry across puzzles

1. Read the goal before you read the start

   How a problem is represented changes how hard it is. In classic work on Tower of Hanoi "isomorphs", puzzles with identical structure but different cover stories, the hardest version took about 16 times longer to solve than the easiest. Before you move anything, describe the goal to yourself in one sentence: "3 at the bottom of peg 1, then 2, then 4", or "the chain must end at exactly 34".

2. Work backwards from the goal

   The last thing to happen is often the most constrained. In a tower puzzle, the bottom disc of each goal peg must be placed first, so start your thinking there. In an arithmetic chain, the final operation tells you what the second-last value must have been. In a maze, ask which cell you must enter the goal from.

3. Find the blocker and where it can wait

   Means-ends analysis in one line: what stops the next goal step, and where can that obstacle go for now? The answer is a subgoal. Parking spots are scarce in most planning games, so choosing the right one is often the whole puzzle.

4. Check for the backward move

   If no move puts a piece straight into its final position, the right move probably takes one away from it. People with weaker planning struggle most with exactly this goal-subgoal conflict. Make "is the correct move a backward one?" a routine question.

5. Plan two subgoals, then re-plan

   Most people can preplan accurately about two subgoals ahead, not three, and instructing people to plan everything up front made them slower without making them more efficient. Plan a chunk you can hold, execute it, then look again.

6. Decide the most constrained thing first

   When several choices interact, fix the one with the fewest options first. Constraint-satisfaction research calls this the fail-first principle. In an arrangement puzzle it is the person with two possible seats; in a chain with blanks it is the blank next to a division.

7. Price reversibility before you act

   Before each move, ask whether you can take it back. Explore freely where undo is cheap. Where it is not, simulate the next few moves first.

A ten-second routine before the first move

Strategies only help if you use them under pressure, so turn them into a routine you run on every puzzle, whatever the game:

1. Goal: say the goal in one sentence.
2. Gap: name the first thing that stands between the start and the goal.
3. Blocker: name what is in the way and where it can wait.
4. Backward check: ask whether the first move has to be a step away from the goal.
5. Count: count your plan against the minimum or the budget.

At first this will feel slow. Within a week or two it becomes quick, and it replaces the impulse to move before thinking. Research on tower tasks suggests the time is well spent: better performers pause longer before the first move and then execute faster.

Reading your own results

Practice only helps if you look at what happened. After each session, our report for the planning games shows figures you can act on:

• Moves beyond the minimum (Towers of London) and committed mistakes (ShiftMaze) count the extra moves you made. If this number is high on puzzles you solved, your first move is usually the problem: you are starting before the plan is complete.
• Puzzles solved or mazes cleared falling while efficiency stays high means the opposite: you are planning well but stalling on the hardest puzzles. Spend longer on the first move of those, and check for a backward move.
• Targets reached exactly (Number Builder) is all or nothing. If it drops at a new level, look at what the level added: a new operator, a third blank or the all-different rule.

Write one line after each session: what went wrong and which strategy would have caught it. Over four weeks that log becomes your personal list of traps, which is worth more on test day than any number of extra sessions.

Carrying the strategies to paper tests

The same moves work on a question paper. In an arrangement set, the fail-first principle tells you where to start. In a CAT reasoning set, working backwards from what each question asks tells you which deductions matter and which you can skip. In a GMAT two-part question, checking what part one forces in part two before you commit is look-ahead. And in any exam with negative marking, pricing reversibility tells you when a guess is worth the risk.

Planning your own preparation

The same research gives you two tools for the real plan that matters this season: your study schedule.

Implementation intentions. A goal ("I will practise reasoning daily") is weak. An if-then plan ("If it is 7 pm on a weekday, then I do two Towers of London sessions before dinner") is much stronger. Across 94 independent tests, forming implementation intentions had a medium-to-large effect on reaching goals, d = .65.

The outside view. People predicting their own project times focus on how the plan should go and ignore how past projects went, so they underestimate. When they were made to connect their estimate to relevant past experience, the optimistic bias disappeared. Before you fix a mock-test schedule, look up how long your last one actually took.

A four-week plan with our games

Short, frequent sessions beat one long weekend block. Each session below takes 10 to 15 minutes. Keep the adaptive setting on so difficulty follows your performance.

1. Week 1: formats
   • Towers of London, 3 sessions: before every first move, say the goal aloud
   • ShiftMaze, 2 sessions: learn the push rules and the corner trap
   • Number Builder, 2 sessions: fill blanks from the target backwards
2. Week 2: backward moves
   • Towers of London, 3 sessions: on each puzzle, ask whether the first move is a backward one
   • ShiftMaze, 2 sessions: before any push, name the cell the crate will land on
   • One timed arrangement puzzle set from a past paper, solved with a case split
3. Week 3: chunks
   • Towers of London, 3 sessions: plan two subgoals, move, re-plan; compare your move counts with the optimum
   • Number Builder and Numerosity, 2 sessions each: most constrained blank first
   • Review your session reports for moves beyond the minimum
4. Week 4: under pressure
   • Mixed planning sessions at your current level, 4 days
   • One full mock of the test you are targeting, with a written plan for which sections or sets to attempt first
   • Write two if-then plans for exam day, for example what you do if a set is not cracking after three minutes

2 practice questions

1. What does the brain-training evidence most strongly support?
2. You can hold about two subgoals in mind. A tower puzzle needs four. What is the best approach?

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Sources

1. Simons, D. J., Boot, W. R., Charness, N., Gathercole, S. E., Chabris, C. F., Hambrick, D. Z., & Stine-Morrow, E. A. L. (2016). Do "brain-training" programs work? Psychological Science in the Public Interest, 17(3), 103–186. doi:10.1177/1529100616661983
2. Sala, G., & Gobet, F. (2017). Does far transfer exist? Negative evidence from chess, music, and working memory training. Current Directions in Psychological Science, 26(6), 515–520. PMC5724589
3. Diamond, A. (2013). Executive functions. Annual Review of Psychology, 64, 135–168. PMC4084861
4. Lowe, C., & Rabbitt, P. (1998). Test/re-test reliability of the CANTAB and ISPOCD neuropsychological batteries. Neuropsychologia, 36(9), 915–923. PubMed 9740364
5. Fimbel, E., Lauzon, S., & Rainville, C. (2009). Performance of humans vs. exploration algorithms on the Tower of London test. PLOS ONE, 4(9), e7263. PMC2748701
6. Unterrainer, J. M., Kaller, C. P., Halsband, U., & Rahm, B. (2006). Planning abilities and chess. British Journal of Psychology, 97(3), 299–311. PubMed 16848944
7. Kotovsky, K., Hayes, J. R., & Simon, H. A. (1985). Why are some problems hard? Evidence from Tower of Hanoi. Cognitive Psychology, 17(2), 248–294. doi:10.1016/0010-0285(85)90009-X. The 16-fold figure is summarised in Kotovsky, K., & Fallside, D. (1988), Representation and transfer in problem solving, in Klahr & Kotovsky (Eds.), Complex Information Processing. PDF
8. Goel, V., & Grafman, J. (1995). Are the frontal lobes implicated in "planning" functions? Neuropsychologia, 33(5), 623–642. PubMed 7637857
9. Phillips, L. H., Wynn, V. E., McPherson, S., & Gilhooly, K. J. (2001). Mental planning and the Tower of London task. Quarterly Journal of Experimental Psychology, 54A(2), 579–597. doi:10.1080/713755977
10. Haralick, R. M., & Elliott, G. L. (1980). Increasing tree search efficiency for constraint satisfaction problems. Artificial Intelligence, 14(3), 263–313. doi:10.1016/0004-3702(80)90051-X
11. Gollwitzer, P. M., & Sheeran, P. (2006). Implementation intentions and goal achievement: A meta-analysis of effects and processes. Advances in Experimental Social Psychology, 38, 69–119. doi:10.1016/S0065-2601(06)38002-1
12. Buehler, R., Griffin, D., & Ross, M. (1994). Exploring the "planning fallacy". Journal of Personality and Social Psychology, 67(3), 366–381. doi:10.1037/0022-3514.67.3.366
13. Unterrainer, J. M., Rahm, B., Kaller, C. P., et al. (2004). Planning abilities and the Tower of London: Is this task measuring a discrete cognitive function? Journal of Clinical and Experimental Neuropsychology, 26(6), 846–856. PubMed 15370380