4Sums · Puzzles

Start here

Welcome to 4Sums! One idea runs through every puzzle: letters are numbers, and words are sums. Find the right words and the numbers fall into place. Here's the whole idea in 30 seconds.

Try one now Try Single Try Reveal Try Junction

A worked example

Target: 17

Try the word TEAM.
T = 20, E = 5, A = 1, M = 13
20 / 5 + 1 × 13 = 4 + 13 = 17 ✔

Every letter has a value — its place in the alphabet: A = 1, B = 2, C = 3 … Z = 26.
Put an operator between the letters: + − × /. The word’s four letters make a small sum.
Hit the target. The puzzle gives you a target number. Your job is to find real four-letter words (and the operators) whose sum lands on it exactly.

The idea in action in Single: a first guess misses, then the real word is typed and the right operators are picked to land exactly on the target.

Where to begin

New here? Play these three first, in this order. Each one teaches one part of the game.

1. Single — the classic. One target, and you find words that reach it before the clock runs out.

2. Reveal — guess a secret word with colour clues, then choose the operators that make it hit the target.

3. Junction — a 4×4 grid of words. Find the one row and the one column that reach the target; they cross at a single letter.

You don’t have to play everything

There’s no need to finish everything every day! Pick a few puzzles or games you like, or even just one, and go from there. If you like Wordle, you might only ever play Reveal; if you’re a fan of bingo, you might stick to Lingo and skip the puzzles altogether. It’s completely up to you.

More than a game

The idea first came from primary school children doing sums with letters while they learned the alphabet code, A = 1, B = 2 and so on. The puzzles are still designed to help with maths and vocabulary, and they also touch on real ideas that are used in practice:

Ciphers and cryptography — keyword ciphers, Caesar shifts, random (substitution) ciphers and polynomials turn up in Keyring, Chain, Scramble, Multiverse and Misturora.
Linguistics and language learning — different languages have different alphabets, so the same letter can have different values. The polyglot puzzles let you compare them.
Hexadecimal numbers — the way computers write colours. Mosaic uses real hex colour codes.
Statistics — mean, median, mode and range, in Statzilla.
Shapes and nets — Cube and Tesserato explore the faces, corners and nets of cubes and the cube’s four-dimensional cousin, the tesseract.

Where a puzzle uses one of these ideas, its own How to play guide introduces it.

Every puzzle has its own How to play guide with a worked example, so you’re never stuck. You can come back to this page any time with the How to play button on the Puzzles menu.

Using the app

A quick tour of the screens you’ll meet, and how to get between them.

The home screen

Puzzles opens today’s puzzles, in four levels. Lingo, Game (the board game) and Club 42 have their own buttons.
About 4Sums is a short introduction. This guide is the longer version.
The cog next to the 4Sums name opens Settings, where you can turn sound and animations on or off.

The Puzzles menu

← Home returns to the home screen, and How to play opens this guide.
Use the level tabs (Novice, Apprentice, Adept, Master) to switch between levels. A small amber dot on a tab means there’s a puzzle in that level you haven’t opened yet today.
The tag chips under the tabs (polyglot, timed, scored, cipher, replayable) are filters: tap one to show only puzzles with that tag and read what it means, and tap it again to clear it.
Each card shows the puzzle’s tags, your progress for today (see “Markers on the cards” below), a countdown to the next puzzle, a Yesterday’s answer link and a Play button.

A puzzle’s start screen

Start begins the puzzle. For a timed puzzle the clock starts at that moment.
How to play opens that puzzle’s own guide: what to do, a worked example and a short video. Tutorial, where there is one, is a hands-on walk-through. It’s just for practice and doesn’t count towards anything.
Puzzle language chooses the language of the words, and so the alphabet and the letter values. Changing it reloads the puzzle.
Challenge mode turns the helper tools off, for when you fancy a tougher test.
← Back to menu returns to the Puzzles menu.

While you play

← Menu (top left) leaves the puzzle. Your progress is kept, but on a timed puzzle the clock keeps running until you come back. The question mark ? (top right) opens the puzzle’s guide.
Type with your keyboard or the on-screen one. When a word is valid, the sum screen opens: choose an operator for each gap, then tap Check. If the sum is wrong you’ll see what it came to instead. It costs you nothing, unless the puzzle’s guide says otherwise.
The tools button (a spanner) opens the helper tools: an alphabet map, a calculator and a word lookup, which also links to Wiktionary. Challenge mode removes them.
If a word isn’t on the puzzle’s word list, the tiles shake and a red message appears. Change a letter or tap Clear word to carry on.
Timers pause when the app is in the background (for example during a phone call).

On a computer you can use the keyboard throughout. On a phone, adding 4Sums to your home screen gives you a full-screen app that also works offline.

How letters become numbers

In English (and French, Dutch, Portuguese) the letters run A = 1 to Z = 26. Accents do not matter: café is just C-A-F-E.

A=1 B=2 C=3 D=4 E=5 F=6 G=7 H=8 I=9 J=10 K=11 L=12 M=13
N=14 O=15 P=16 Q=17 R=18 S=19 T=20 U=21 V=22 W=23 X=24 Y=25 Z=26

Between the four letters sit three operators from + − × /. Depending on the puzzle you either choose the operators or are shown them; the sum itself always works the same way. Results can be bigger than you expect, because × multiplies letter values (15 × 18 = 270).

Order of operations (BIDMAS)

BIDMAS tells you which part of a sum to do first: Brackets, Indices, Division and Multiplication, then Addition and Subtraction. 4Sums sums have no brackets or powers, so the rule is short: × and / first, then + and −. Where operators are of the same kind, work from left to right.

Example 1: multiplication first

CODE: C = 3, O = 15, D = 4, E = 5
3 + 15 × 4 − 5
Step 1, the × first: 15 × 4 = 60
Step 2, what is left: 3 + 60 − 5
Step 3, left to right: 63 − 5 = 58

Don’t just go left to right: that would give (3 + 15) × 4 − 5 = 67, which is wrong.

Example 2: exact division

TEAM: T = 20, E = 5, A = 1, M = 13
20 / 5 + 1 × 13
Step 1, / and × first: 20 / 5 = 4 and 1 × 13 = 13
Step 2: 4 + 13 = 17

Division must come out exact. 20 / 5 = 4 is fine, but 20 / 6 is not a whole number, so that choice is simply not allowed. There are never fractions or decimals. With / and × side by side, go left to right: 24 / 4 × 3 = 6 × 3 = 18.

Don’t fancy doing the arithmetic yourself? The helper tools (the tools button in each puzzle) include an alphabet map, a calculator and a word lookup.

Languages and alphabets

Each language has its own alphabet, and letters are always numbered in that language’s own order. So a letter’s value depends on the language you are playing in:

English, French, Dutch, Portuguese, Indonesian: 26 letters, A = 1 to Z = 26.
Spanish: 27 letters. Ñ comes after N (N = 14, Ñ = 15), so O to Z are 16 to 27.
German: 30 letters. Ä Ö Ü ß come after Z: 27, 28, 29, 30.
Swedish: 29 letters. Å Ä Ö come after Z: 27, 28, 29.
Italian: only 21 letters (no J, K, W, X, Y), so Z = 21.
Polish: 32 letters. Accented letters sit right after their base letter (A = 1, Ą = 2, B = 3, C = 4, Ć = 5 …), up to Ż = 32.
Turkish: 29 letters. No Q, W, X; Ç Ğ İ Ö Ş Ü are added, and dotless ı and dotted i are separate letters (A = 1, B = 2, C = 3, Ç = 4 …), up to Z = 29.
Swahili: 24 letters (no Q, X), so Z = 24.

Same letter, different value: O is 15 in English, 16 in Spanish and 13 in Italian. The alphabet map in the helper tools always shows the right values for the puzzle you are playing.

You choose the language of the words with the Puzzle language drop-down on each puzzle’s start screen. The menus, puzzle names and help are always in English.

Letters and accents

An accent (the proper word is diacritic) is a mark added to a letter, like the é in café. It is not a letter in its own right. Some languages treat a marked character as a separate letter of their alphabet, so it gets a number of its own: German has ä ö ü ß, Spanish has ñ, and Swedish has å ä ö. Other languages, such as French, Portuguese, Dutch and Italian, use the same basic letters as English and then add accents on top of them, and those accents do not count as new letters.

In 4Sums the words in those languages are written without their accents (café becomes CAFE). That was partly a choice, to show the difference between a letter and a mark added to a letter, but mainly a practical one: each letter gets its number from its place in the alphabet, and an accent is not in the alphabet, so it would confuse the system. It is a compromise. If you look a word up on Wiktionary from the helper tools, you will see the accents there.

What does “polyglot” mean?

🌐 A polyglot puzzle uses several languages at once (up to all twelve), whatever puzzle language you have selected: Eingle, {name:intersecto}, Signisenso, Squadrada, Ruticulo, Misturora, Tesserato and Verticume. In most of them each word is in its own language and counted with that language’s own alphabet. They are the best place to show off your vocabulary.

Verticume and Misturora go one step further and share one combined 45-letter alphabet, so a word from any language can sit in the same grid:

A=1, Ą=2, B=3, C=4, Ć=5, Ç=6, D=7, E=8, Ę=9, F=10, G=11, Ğ=12, H=13, I=14, İ=15, J=16, K=17, L=18, Ł=19, M=20, N=21, Ñ=22, Ń=23, O=24, Ó=25, Ö=26, P=27, Q=28, R=29, S=30, Ś=31, Ş=32, T=33, U=34, Ü=35, V=36, W=37, X=38, Y=39, Z=40, Ź=41, Ż=42, Å=43, Ä=44, ß=45

This combined alphabet is itself an example of how alphabets, letters and languages work. No such alphabet exists in real life: it was invented for this app. It follows the same idea as systems like Unicode, which gives every letter from every language its own number, so that computers can store and show text in all of them together.

All the puzzles

There are four levels. Start at Novice and work up when you fancy a bigger challenge.

Tags on each card: 🌐 polyglot (up to twelve languages), ⏱ timed (a countdown), ★ scored (you earn a score), ↻ replayable (a daily puzzle you can replay for practice).

Novice

Quick puzzles, and the best place to start.

Single ⏱ ★ — find four different words that reach today’s target before the timer runs out. At weekends it is a “Unique” puzzle: just one word to find.
Junction ⏱ ★ — a 4×4 grid of words; find the one row and the one column that reach the target, where they cross.
Reveal ★ — guess the secret four-letter word using colour clues, then pick the operators so it reaches the target.
Matches ★ — four words and four numbers: only four of the sixteen pairings are real. Test pairs until you have found all four.
Eingle 🌐 ⏱ ★ — one target and four word slots, one per language; fill each with a word that reaches it.
Signisenso 🌐 ⏱ ★ — two words in two languages that mean the same thing; find four numbers that both words can make.

Apprentice

A step up: more letters to place, or several words at once.

Square — four words around a frame (top, left, right, bottom), sharing letters at the corners, all reaching one target.
Keyring — four words around a frame, all reaching one target — but the alphabet changes as you go. Lock in the left word and its letters become a keyword that renumbers the alphabet for the top word, then the right, then the bottom.
Statzilla — four overlapping squares, each judged by a statistic (such as the average) instead of a plain sum; the four results lead to one last answer.
Cube — type letters into the eight corners of a cube so that each of the six faces can be rearranged into a word that reaches the shared target.
{name:intersecto} 🌐 ★ — a 4×4 grid in which every row and column is a word, in just four languages: find where each language’s row and column cross, then make four sums per direction reach one shared number.
Squadrada 🌐 — a square frame of four words, each side in its own language, all reaching the same target.

Adept

Big grids, several targets and scrambled alphabets.

Quadzilla — four Square puzzles joined into one big shape, with a target for each. Slow and satisfying.
Gridlock — fill a 4×4 grid so that every row and column is a word: rows reach one target, columns reach another.
Scramble — the alphabet has been secretly renumbered. Work out the new letter values from the solved examples, then find the word. (Not available in Italian: see the FAQ.)
Multiverse — one secret word has to solve four number puzzles at once, because each one values the letters differently.
Ruticulo 🌐 — a Gridlock grid in which every row and every column is in its own language.
Tesserato 🌐 — eight cube puzzles, one per language, linked so that neighbouring cubes share a face that spells the same word in both languages.

Master

The deepest puzzles: each one is a proper project.

Chain — a Quadzilla was solved in a secret order, each word’s letters feeding a keyword cipher for the next. Decode the order and reveal the mapping.
Mosaic ★ — an 8×8 grid of jumbled tiles hides sixteen words. Swap tiles, lock in words, and colour strips reveal the picture.
Summit — fill an 8×8 grid; blocks become words, words become numbers, and everything boils down to one final word that hits an exact target. (English, German, Dutch and Swedish.)
Verticume 🌐 — the polyglot Summit: the same rules, but words come from any of the twelve languages and the alphabet has 45 letters. It takes the place of Summit in French, Spanish, Italian and Portuguese.
Misturora 🌐 — one secret cipher shared by all twelve languages: the 45 letters get random values, and you have to deduce them.
Patchwork — one 7×7 board that weaves four puzzles together: a Gridlock, a Keyring, a statistics square and a Junction, sharing words along their edges. Twenty words, five targets, and some letters given.

Recommended path

Novice: Single → Reveal → Junction → Matches → Eingle → Signisenso
Apprentice: Square → Keyring → Statzilla → Cube → {name:intersecto} → Squadrada
Adept: Quadzilla → Gridlock → Scramble → Multiverse → Ruticulo → Tesserato
Master: Chain → Mosaic → Summit → Patchwork → Verticume → Misturora
And for fun, anywhere along the way: Lingo and the 4Sums board game. Once you know the puzzles well, give Club 42 a go.

Playing

Pre-filled letters and randomness

In many grid-style puzzles some tiles start already filled in. They show in amber. Which tiles, and how many, is chosen at random every time you start, so you never get exactly the same start twice.

Playing again

When you finish a puzzle, Play again lets you practise: the same targets, but a different pre-filled start (a different valid solution where there is one). Replays aren’t scored and never change your score, timer or card markers. Only your first go counts.

Scores and timers

Scored puzzles give you a result such as 3/4 (words found out of four). Timed puzzles have a countdown; when it ends you keep what you found. Only your first attempt of the day (or of the puzzle’s run) is recorded.

Multi-day puzzles

Some puzzles stay the same for several days, because there are fewer of them or they are very hard to make. The card says “New puzzle in N days” (or “tomorrow”), your progress is kept until it changes, and the answer link reads “Previous answer” rather than “Yesterday’s answer”.

Markers on the cards

In progress (amber): you have started it, sometimes with a count such as 2/4.
Solved (green): finished with a full score.
Done · 3/4 (green): finished with a partial score.
Attempted: finished with no points, for example when time ran out.
↻ Replayable: a daily puzzle you can play again for practice once you have finished it (the Play again button).
The small amber dot means a puzzle you have not opened yet today.

Challenge mode and helper tools

Every start screen has a Challenge mode switch. On, it switches the helper tools off (alphabet map, calculator, word lookup) for a purer test. Off, you can open them any time from the tools button .

Yesterday’s answers

Stuck, or just curious? Each card has a Yesterday’s answer link (or Previous answer) that shows the full solution to the last puzzle.

Lingo

Lingo is the number-card game. Instead of finding the word for a target, a four-letter word is shown to you and you look for a number on your card that its letters can make. It comes in three modes, chosen in the game options: Classic, Bingo and Tournament.

Your card and the words

Your card is a 4×4 grid of 16 different numbers between 1 and 100. Some carry a ×2 or ×4 badge: they are the hardest to make, so they score more. Every word has four letters, each worth its place in the alphabet. Put + − × or ÷ between the letters (× and ÷ first, and a division must come out exactly) and see whether you can land on one of your numbers. You do not have to type the sum: just tap the number and the game shows the working.

TIME = 20, 9, 13, 5
20 + 9 + 13 × 5 = 20 + 9 + 65 = 94

Classic

One tap per word. A correct tap crosses the number off. A wrong tap scores nothing and locks that number in red for the rest of the game. If you cannot see a match, press No match · next word: it costs nothing.
Scoring: 1 point per number, +4 for each row or column you complete, +16 for the full house. A ×2 or ×4 number multiplies everything you score on that turn.
The clock is a time bank. There are 24 words and you choose 20, 30 or 40 seconds per turn. Time left over carries on to the next word. If the clock runs out the game ends and you keep your score.

Bingo

One word at a time is called to you and to 15 computer players, each with their own card. There are no multipliers and no word limit: the first player to cross off all 16 numbers wins. A wrong tap only costs you that word. As in real bingo, you cannot see how the other players are getting on: the suspense is part of the fun.

Tournament

A series of bingo games for counters against the same 15 players. Before every round each player chooses their own bet, from 2 to 8 counters (the computer players bet according to their personality), and the bets make the pot. The first to complete a line wins 10% of the pot, the first with two lines wins 20% of what is left, and the first to the full house takes the rest. The player with the most counters after the last round is the champion.

Open Lingo

An explained playthrough of Lingo: crossing numbers off the card with the words.

The board game

The puzzle as a board game. Roll the die and move your four counters onto letter squares. The goal is to get all four onto different letters that spell a real word whose letters reach the target, then claim the win and prove it with the right operators. Land exactly on an opponent to send them back; a wrong claim costs you a turn.

Players. You play against computer opponents (three on the standard board, seven on the double board). Each has a name and a character of its own: a word knowledge level and a personality (thoughtful, balanced or impulsive), which are the same in Lingo and Club 42. Type your own name in the options before you start.
Teams. In team games partners share one word. A key under the target number shows each team as a round marker split in two colours, the colours of its two players.
Options. Language (any of the twelve, or Polyglot), turn time, target range, letter values and the helper tools, plus a Tournament mode played for tokens.

Open the board game

A game of the 4Sums board game explained: the options, a human turn, the computer players, and a winning claim.

Club 42

Club 42 packages up lots of the puzzles, the board game and a brand-new grid idea into a single game experience: you arrive at a party, wander a letter grid of words and sums, take on hosts and guests in puzzle challenges, and finish with a midnight tournament.

It’s designed for players who already know the puzzles, so it’s not really one for beginners — we recommend getting the hang of all the puzzles individually first.

A new party opens every day. Your progress is saved on this device until the next day’s party, then cleared when the new party becomes available, or earlier if you clear your browser’s cache or site data. You arrive at the party at 10pm, which gives you 2 hours to complete the grid before the midnight tournament. The other guests take between 60 and 120 minutes, so keep moving!

Open Club 42

A fully explained playthrough of Club 42: tracing words across the grid, and how the cipher, multiplier and polyglot sectors each change the rules.

Questions and answers

Where do the words come from?

Each language has its own curated list of four-letter words. English uses standard US and UK dictionary word lists (about 4,800 words). French, Spanish, German and Dutch start from a curated dictionary list, Italian from a hand-checked list verified against a Scrabble word list, Swedish from a spell-checker dictionary, and Portuguese from a curated dictionary extended with a larger word list covering Portugal and Brazil. Word-frequency lists (for the other languages drawn largely from film and TV subtitle text) are used to rank how common each word is.

How were the word lists cleaned up?

Every list goes through the same filters:

only four-letter words, using only letters from that language’s alphabet (see “Why do some languages keep their accents and others do not?” below);
no numbers, hyphens, web addresses or other non-words, and no letter repeated three times in a row (such as “hmmm” or Roman numerals);
rude and swear words removed: explicit, vulgar and hateful words are filtered out using a built-in list for English and a separate list for each other language (mild words such as “damn” are allowed);
words that are only names, and words that leaked in from other languages, are removed.

We’ve been careful, but it isn’t perfect. If you spot a word that shouldn’t be there, or one that’s missing, we’d love to know.

Which words are left out?

Words that are only names (of people or places), and rude or swear words, are left out. If a name also means something else it can still be present: Anna is a name, but it is also a type of historical coin, so it counts as a valid word. If you are not sure whether a word is included, look it up in the helper tools, or just try it: the puzzle will usually tell you. Some very recent new words may not be on the word lists yet, so check those in the helper tools first.

Do the puzzles use rare words?

Sometimes, yes. Rarity is a personal thing: even the most common 20% of a language contains plenty of words that people rarely use. Most puzzles are made to favour common words that the average person knows, but some use the full word list when they have to, especially the more complex grids such as Gridlock and Junction and the large puzzles that include them. It is very hard to find lots of words that overlap in so many ways and still all be real words. So you will now and then meet a “Scrabble word”: an obscure, technical, archaic or dialect word you may not recognise. The helper tools show the full word list, with a link to Wiktionary for every word (Wiktionary is edited all the time, so we cannot promise every link will always work). On the bright side, you’ll pick up a few odd words you never knew existed.

Why isn’t my word accepted?

Check these first. Is the Puzzle language on the start screen the language of your word? (Polyglot puzzles accept all twelve.) Is it exactly four letters? Names, abbreviations, plurals, conjugated forms and very rare or very new words may not be on the list. Use the Word lookup helper tool to see which words are on the list for your language. English accepts both UK and US spellings where both have four letters (grey and gray, tyre and tire). Because the lists are curated, a perfectly real word can occasionally be missing. A rejected word makes the tiles shake and shows a red message; it never costs you a guess or a point.

Why only four letters?

Every sum has exactly four letters and three operators. That keeps each puzzle small enough to check at a glance, large enough to be a challenge, and it gives the app its name.

Why do some languages keep their accents and others do not?

Accents (diacritics) are marks added to letters; they are not letters themselves. German, Spanish and Swedish count characters like ä, ö, ü, ñ and å as separate letters of their alphabets, so they have numbers of their own. French, Portuguese, Dutch and Italian use the same basic letters as English and add accents on top, so in 4Sums their words are written without accents. That was partly a choice, to highlight the difference between a letter and a diacritic, but mainly a practical one: letters get their value from their place in the alphabet, and accents are not in it, so they would confuse the system. If you look a word up on Wiktionary, you will see it with its accents there.

Why do the polyglot puzzles have odd names?

They are portmanteau words, made by blending translations of an English word that describes the puzzle, taken from different languages. For example, Zungua is a mash-up of Zungen and lingua, which mean “tongues” in German and Italian. Tongues fits a puzzle about spotting words across languages nicely.

Which languages can I play in?

The word lists cover English, French, Spanish, German, Italian, Dutch, Portuguese, Swedish, Indonesian, Polish, Turkish and Swahili. Choose the language on the puzzle’s start screen; the choices shown are the ones available for that puzzle. A polyglot puzzle (look for the 🌐 tag) uses several languages at once, up to all twelve. A few puzzles are not available in every language. Scramble needs a big pool of words, so it is missing in Italian (the smallest list, with only 21 letters) and Polish. Summit needs a lot of four-letter words with no repeated letters in a group, which the French, Spanish, Italian and Portuguese lists cannot supply, so those languages get Verticume, which uses all twelve languages, instead.

When do the puzzles change, and why do some last several days?

New puzzles arrive at midnight on your device’s clock, wherever you are, and the menu shows a countdown. Unfinished progress on a daily puzzle is cleared at the change. The puzzles are made in advance: for most types there are well over a thousand in English, enough for several years of daily play. In a few languages, some types (such as Chain and Scramble) are very slow to make and check, so there aren’t enough for a new one every day. In those languages the puzzle stays live for a few days and keeps your progress; the start screen and the card tell you when the next one arrives.

Is my progress saved?

Yes, but on this device and browser only. There are no accounts and nothing is sent anywhere. That means progress does not move to another device, and clearing your browser data (or playing in a private window) erases it.

Is there a tutorial?

Yes. The Tutorial button on the start screen of each supported puzzle (and of Club 42) gives an interactive step-by-step walk-through on a fixed example. It’s just for practice and doesn’t count towards anything (no streak, score or progress).

Why are the menus and help only in English?

The puzzles can be played with words in many languages, but the app’s own text (menus, puzzle names, help and tutorials) is in English for now, so that everything you read has been checked. Translations of the interface exist but are switched off until they have been proofread.

Can I install it and play offline?

Yes. Use your browser’s Install or Add to Home Screen option (on iPhone: Share, then Add to Home Screen) and 4Sums opens full-screen, even when you’re offline.