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Make the target

Four numbers and a target, 24-game style: which expression uses each number once and hits it? More numbers, bigger ones, all four operations.

  • Calculation
  • Untimed
  • Endless levels

How it plays

You are given some numbers and a target. Several expressions are offered; exactly one uses every number once — no more, no less — and makes the target. Find it.

The others are near misses: one operator changed, one number used twice (sometimes reaching the target anyway, which is why you must check the numbers too), or the brackets forgotten so × is done before +.

Levels add numbers (up to six), make them bigger without limit (five more a notch), and bring in × and then ÷. The working evaluates the right one step by step and says what is wrong with each of the others.

Keys

Space starts and skips ahead · 1–9 pick · Enter submits · Esc stops. On a phone, tap.

What it trains

This practises checking expressions — order of operations, and whether a solution uses what it was given. It is practice at this task, nothing wider.

Learn

How to get better at make the target: the method, the techniques, what each new level asks of you, and the traps the wrong answers are made of.

Your approach to each question

  1. Check the numbers before the arithmetic. Each option must use every given number exactly once; an option that does not is out, however good its value.
  2. Look for two options with the same numbers and signs in the same order, one with brackets and one without. One of them is the brackets-dropped lure; only working out tells you which.
  3. Evaluate what is left, brackets first, then × and ÷, then + and − from left to right.
  4. Stop as soon as one survivor hits the target. Exactly one option is right, so you do not need to finish the others.

Techniques and tricks

  • Compare the number sums

    Add up the numbers written in an option and compare with the sum of the given numbers. Using one twice and leaving another out changes that sum, so a mismatch rules the option out in seconds.

    e.g. Given 12, 1, 11, 19, 19, 6 (sum 68): “1 + 11 + 6 + 19 + 1 − 12” has numbers summing to 50, so it is out.

  • Tick off the one you choose

    Before you commit, read your chosen option once more and tick each given number off the list as you meet it. Every number should be ticked exactly once, with none left over.

  • Whole numbers all the way

    The right expression is built so that every step is a whole number of zero or more. An option where a step gives a fraction or drops below zero is a lure.

    e.g. “6 ÷ 19” inside an option makes a fraction, so that option is wrong.

  • × and ÷ before + and −

    Without brackets, do every × and ÷ first, left to right, then the + and −. Brackets change that order, which is exactly what the dropped-brackets option tests.

    e.g. 11 + (12 + 17) × 14 ÷ 7 − 6: 29 × 14 = 406, ÷ 7 = 58, 11 + 58 − 6 = 63.

  • Size and last digit

    Before working an option fully, estimate it and check its last digit against the target’s. A changed operator usually moves the size a long way or changes the last digit.

As the levels climb

  • Numbers come first: 4 at level 0, 5 at level 1, 6 at level 4, up to the “Most numbers” setting. More numbers means more to tick off, so do the number check before anything else.
  • The biggest number rises by 5 a notch without end: up to 9, then 14, 19, 24 and on. Larger numbers make the size check stronger and full evaluation slower.
  • With the default “+ − first, then ×, then ÷”, × arrives at level 3 and ÷ at level 6. Before ×, a dropped bracket only changes what a minus covers; after it, the order of operations starts to matter too.
  • At ÷, fractions appear in the wrong options. The whole-numbers rule becomes the fastest filter you have.

Traps to avoid

  • A number used twice that still makes the target. Its value checks out, which is the point; only the number check catches it.
  • The brackets dropped: the same numbers and signs, so a minus no longer covers the whole bracket, or a × is now done before a +. Work it with the precedence rules, not left to right.
  • One operator changed, + for −, × for ÷. Its value is usually far from the target, so the size check catches it before you evaluate it.
  • A number used twice that does not make the target: the number check and the value both rule it out, so check numbers first and save the arithmetic.

How to practise

  • Set Operations to “All four from the start” once the + and − levels are easy, so you meet the precedence lures sooner.
  • Lower “Most numbers” to 4 to drill the checks on short expressions, then raise it back to 6.
  • Raise “Options shown” to 6 or 8 for more lures to rule out; it trains the number check rather than the arithmetic.
  • When you pick wrong, read the working’s line for that option: it names the slip, and the slip tells you which check you skipped.

Levels

It is untimed unless you turn the clock on. There is no last level: at least one dial turns without end. Your level is judged on your last ten answers, every ten: 90% moves you up, below 80% moves you down, which holds most people near four in five right.

All of it is in the settings beside Start — how many answers a judgement looks at and how often it recalibrates, the thresholds, the time, which questions, how many options, and whether you see each verdict at once or review them together at the judgement. You can also jump to any level.

More calculation

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