Turn four digits into a true equation
You get four digits. Keep them in the order they're printed, use each one exactly once, and place a single = sign so both sides come out equal. Every one of the 10,000 possible plates, from 0000 to 9999, has at least one solution.
1372
1 = 3! − 7 + 2
3! is 6, and 6 − 7 + 2 = 1. The = sign can go after any digit.
Allowed operations
| Symbol | What it does | Example |
|---|---|---|
| + − × ÷ | Add, subtract, multiply, divide | 8 ÷ 2 = 4 |
| − | Negative sign in front of a number or group | −1 + 3! = 7 − 2 |
| ( ) | Group anything | (4 + 4) × 2 |
| 47 | Join neighbouring digits into one number | 12 = 8 + 4 |
| .7 | Put a decimal point in a digit or joined number | 5.2 = 3! − .8 |
| ^ | Power, using a digit or expression as the exponent. A fraction as the exponent takes a root, like 8^(1 ÷ 3) = 2 | 7^2 = 49 |
| √ | Square root | √9 = 3 |
| ⁿ√ | nth root, with the index from the plate: type the index digits, then press ⁿ√ (or type root). Any index except 0, and odd roots of negatives are fine | ³√8 = 2 |
| ! | Factorial: 5! = 5 × 4 × 3 × 2 × 1. Also 0! = 1 | 3! = 6 |
| !! | Double factorial: multiply every other number down | 7!! = 7 × 5 × 3 × 1 = 105 |
Not allowed
- Reordering digits, skipping one, or using one twice.
- Adding any number that isn't on the plate. Exponents are fine when the exponent comes from the plate (
7^2on a plate with a 7 then a 2), but4²on its own adds a new 2. - Joining or splitting results. If you work out 4 × 7 = 28, it's just 28: you can't split it into 2 and 8, glue it to another number, or turn it into .28.
- A whole number that starts with 0, like
07. Decimals such as0.7and.07are fine. - A 0th root, like
⁰√8.
How symbols combine
- × and ÷ happen before + and −, as usual.
- √ applies to the number or bracket right after it, so
√9!means(√9)!= 6. Write√(9!)for the root of 9!. nth roots work the same way:³√8!is(³√8)!. - The ⁿ√ key turns all the digits just before it into the index, so 2, 3, ⁿ√, 8 makes
²³√8, the 23rd root of 8. Write2 × ³√8to multiply. The √ key is always a square root. - A leading minus applies after factorials and powers:
−3!is −6 and−2^2is −4. Write(−2)^2for 4. - ^ comes before × and ÷ and groups from the right, so
2^3^2is 2^9. Factorials happen first:2^3!is 2^6. - You can type
*orx,/,-,**andsqrt; they turn into × ÷ − ^ √ as you type, and3root8becomes³√8. The keys under the input box add the special symbols. - A bar over the top shows what each √ covers.
Difficulty levels
Levels come from solving all 10,000 plates by computer. Each plate's answers are grouped into ideas (moving a number across the = or flipping every sign doesn't make a new one), and the level depends on the tools the easiest idea needs and how many different ideas there are.
With Random picked, the Tools I'll use switches leave out plates that need a tool you've switched off. Hints and Show answer then stick to the tools you've left on, and in Restricted the switched-off keys are grayed out too. Fractional powers count as ^. Eco ignores the switches, since its shortest answers can use any tool.
Challenge modes
Pick a mode with the Challenge switch under the difficulty buttons. Points and streaks are shared across modes.
- Normal: any correct equation scores, and the Left and Right totals update as you type.
- Restricted: use only the tools the plate needs. Keys the level never needs are switched off, and typing them doesn't work either: on Easy only + − × ÷ work, and on Medium and Hard the Expert tools are off. If your answer uses a tier the plate doesn't need, like √ on a plate that works with + − × ÷, you're asked to try again for the points. Hints point to an answer within the plate's tools.
- Eco: find an answer with the fewest operations. A counter shows how many you've used, and the Show goal sticker in the plate's top-left corner reveals the target. An answer that works but uses more operations than the goal doesn't score yet. Hints point to a shortest answer, and every key stays on, since the shortest answer can use any tool.
- In Restricted and Eco the running totals are hidden, and a wrong answer just says "Not balanced".
The tools come in three tiers, and the keypad groups its keys the same way: Basic (+ − × ÷, minus signs, brackets, joined digits), Advanced (√ ! ^) and Expert (a decimal point, !!, nth roots, and fractional powers like 8^(1 ÷ 3)).
Scoring
- Solving earns 1 point on Easy, 2 on Medium, 4 on Hard and 6 on Expert. A Random plate, or one you type in yourself, earns the points for its real level.
- There are four hints, each more specific than the last: which advanced tools you can't do without, where the
=goes, exactly which operations it uses, and what both sides equal. In Eco they point to a shortest answer instead. Each costs 1 point from that puzzle, but a solve is always worth at least 1. - Showing the answer or skipping to a new puzzle ends your streak.
- Any correct equation counts, not just the one the game has on file.
- After you solve or show the answer, you'll see the most basic answer and, when a different one is shorter, the one with the fewest operations. Every symbol counts as an operation except brackets and the
=sign. - Most basic means + − × ÷ alone if that works, otherwise the easiest level of tools that does. Ties go to the lowest score, where + − × ÷ score 1, √ ! ^ score 2, and . !! nth roots and fractional powers score 3, then to the answer with the least work under √ and ! (
√(2 + 6 ÷ √9)is harder than(√9)!).
Where the plates come from
Each new plate is issued by one of these states, picked at random. About 1 plate in 20 turns up at night.
| State | Slogan | A riff on |
|---|