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expressionshow to play expressions

Expressions is an arithmetic game. You get four numbers and a board of targets from 0 to 31. Your job is to hit as many of those targets as you can, combining all four numbers into one expression with +, −, × or ÷.

There is no single right answer. Some of the 32 targets can't be made from a given day's numbers, and the ones that can usually have several routes to them. Your score is the number of targets you find.

the rules

use all four

Every attempt uses each of the day's four numbers exactly once.

two at a time

You only ever combine two numbers at a time. Four become three, then two, then one, and that last number is the result.

order matters

For − and ÷, the number you pick first is the one being subtracted from or divided. + and × are associative.

whole number at the end

Fractions and negatives are fine along the way, but the last number has to be whole and positive.

a worked example

Let's find two of the possible target numbers using 4, 10, 12 and 13.

  1. 4
    10
    12
    13

    The board shows every possible target from 0 to 31. The four dimmed targets can't be made from these numbers, so 28 targets are in play.

  2. 4
    212 − 10
    13

    Tap 12, then −, then 10, and the two merge into 2. Tapping 10 first would have made −2 instead.

  3. 8(12 − 10) × 4
    13

    Combine that 2 with the 4 (using ×) to make 8.

  4. 21(12 − 10) × 4 + 13

    8 + 13 leaves one number, so the round is over and 21 is found!

  5. 8(12 − 10) × 4
    13

    Press undo to split the numbers you just merged. 21 stays found.

  6. 513 − (12 − 10) × 4

    Subtract the 8 from the 13 instead, and the same opening finds a second target: 5.

controls

Tap a number, tap + − × or ÷, then tap a second number. The two collapse into one number holding the result.

You can also drag one number onto another to pick both at once. The one you drag is the first of the two.

If using a keyboard: type 1 to 4 pick the numbers from left to right, + - * and / for the operators, backspace to undo, and escape to drop the current selection.

tips

  • Work backwards from one target. Pick an open target and ask what last step could land on it: 21 could be 8 + 13, or 3 × 7, or 24 − 3. Then check whether the four numbers can build one of those pairs.
  • Make a 1 or a 0. Two numbers that differ by one give you a 1 (via −). Two of the same numbers can give you 1 (via ÷) or 0 (via −). This is sometimes helpful in narrowing towards a target.
  • Use undo to unmerge two numbers. This can be a faster way to combine the same two numbers in multiple ways.