Countdown Solver: The Numbers and Letters Games

A countdown solver is anything that finds an answer to the two puzzles at the heart of the game Countdown: the numbers round, where you hit a three-digit target using six given numbers, and the letters round, where you make the longest word you can from nine chosen letters. Some solvers are software. Some are a pencil, a scrap of paper, and thirty seconds of clear thinking. This guide is about both, and mostly about the second.

The game comes from the British quiz show of the same name, itself adapted from the French format Des chiffres et des lettres. But you don't need a television to play it. The numbers game is one of the best mental arithmetic exercises ever designed, the letters game is a genuinely good anagram workout, and both work fine on a kitchen table with a timer. What follows is the rules, the math, and the habits that let people solve these things by hand.

What a countdown solver does

A countdown solver takes the six numbers and the target and searches for an arithmetic expression that reaches it, or takes nine letters and returns the longest words that can be built from them.

The two halves work completely differently.

A numbers solver is a search problem. It builds every valid combination of the six numbers with the four operations, prunes anything invalid, and checks the results against the target. There are only a few hundred thousand distinct expressions, which is nothing for a computer and enormous for a person.

A letters solver is a lookup problem. It sorts the letters of every word in a dictionary alphabetically to make a key, stores them all, then sorts your nine letters and checks every subset against that index. It doesn't search at all. It just looks things up very fast.

The human versions of these tasks are nothing like either. People don't search exhaustively and they don't hold a dictionary in memory. They pattern-match, and the whole skill is in knowing which patterns to look for first.

The numbers game: the rules exactly

Six numbers, one three-digit target, thirty seconds, four operations, and every intermediate result must be a positive whole number.

The full rules:

• The pool is twenty-four small numbers (two each of 1 through 10) and four large numbers (25, 50, 75, 100).
• You choose six in total, deciding how many large ones you want, from none up to four. The rest come from the small pool.
• A random target between 101 and 999 is generated.
• You may use +, −, ×, and ÷.
• Each of the six numbers may be used at most once. You do not have to use them all.
• Every intermediate value must be a positive integer. No negative numbers, no fractions. 10 ÷ 4 is not allowed. 10 − 15 is not allowed.
• Scoring: 10 points for hitting the target exactly, 7 for landing within 5, 5 for landing within 10. Beyond 10 away, nothing.

That partial-credit structure changes how you should play. Getting close is worth most of the value, so a rough answer you're sure of beats an exact answer you don't find in time.

How to solve the numbers round by hand

Anchor on a multiple you can build easily, then trim the difference with what's left over. That single habit solves most rounds.

Almost nobody solves these by trying combinations at random. The reliable method is:

1. Look at the target's rough size. 887 is roughly 900. 424 is roughly 400 or 425.
2. Find a product in your numbers that lands near it. With 100 in hand, any multiplier from 2 to 9 gives you 200 through 900 immediately. With 75, you get 150, 225, 300, 375, and so on.
3. Compute the gap between that product and the target.
4. Build the gap from the numbers you haven't used.
5. Add or subtract it.

Worked example. Numbers 100, 75, 10, 9, 4, 1, target 887.

• 887 is near 900. And 900 = 100 × 9. Use both.
• The gap is 13, and you need to come down. You have 75, 10, 4 and 1 left.
• 10 + 4 = 14, one too many. But 10 + 4 − 1 = 13.
• So: 100 × 9 = 900, then 900 − 10 − 4 + 1 = 887.

Written out: (100 × 9) − 10 − 4 + 1 = 887. The 75 goes unused, which is completely fine.

Second example, same method. Numbers 50, 8, 7, 3, 2, 1, target 424.

• 50 × 8 = 400. Gap of 24.
• 7 × 3 = 21, plus 2 plus 1 = 24.
• (50 × 8) + (7 × 3) + 2 + 1 = 424.

The factoring approach

When the target has a friendly factor, build that factor and multiply up. This is where the elegant solutions come from.

Numbers 100, 9, 7, 5, 3, 1, target 763.

Rather than reaching for 700 and trimming 63, notice that 763 = 7 × 109. You have a 7. And 109 = 100 + 9, both of which you have.

(100 + 9) × 7 = 763. Three numbers, done.

To use this, you need a quick sense of divisibility:

• By 2: ends in an even digit.
• By 3: digits sum to a multiple of 3. 763 → 7+6+3 = 16, so no.
• By 5: ends in 0 or 5.
• By 9: digits sum to a multiple of 9.
• By 11: alternating digit sum. For 913: 9 − 1 + 3 = 11, so yes, 913 = 11 × 83.

Testing 7, 11 and 13 on a three-digit target takes a few seconds each and pays off often, because the quotient is usually a two-digit number you can build from a large number plus a small one.

The 25/50/75/100 relationships

The four large numbers combine into a lot of round values, and knowing them cold saves you five seconds every round.

• 75 + 25 = 100
• 100 − 25 = 75
• 50 + 25 = 75
• 100 + 75 + 25 = 200
• 75 × 4 = 300, 75 × 8 = 600
• 25 × 4 = 100, 25 × 8 = 200, 25 × 12 = 300
• (100 + 25) × 8 = 1000, useful when the target is in the 900s and you'll subtract

That last one is worth remembering. Targets in the high 900s often come out easier from above than from below.

When you can't get there

Take the partial points. Seven points from a near miss beats zero from a search that ran out of time.

Numbers 9, 8, 6, 5, 4, 3, target 947. No large numbers, which makes high targets awkward.

• 5 × 4 × 6 × 8 = 960. That's a solid anchor built from four of your numbers.
• Gap: 13 down. Remaining numbers are 9 and 3, which give you 12 or 27 or 6.
• 960 − 9 − 3 = 948. One away from 947, so 7 points.

Say that answer out loud with confidence and move on. Spending the last ten seconds hunting for exact usually costs you the near miss as well.

The habits that separate good solvers from slow ones

• Write the numbers down in a row and cross them off as you use them. Reusing a number by accident is the most common mistake there is.
• Say the target's neighbors to yourself. For 887 that's 880, 890, 900. One of them is usually reachable.
• Compute the gap early. Knowing you need "13 more" narrows the search enormously.
• Don't be afraid of subtraction. Beginners overwhelmingly build from below. Overshooting and trimming is often shorter.
• Remember you can ignore numbers. A three-number solution is worth exactly the same as a six-number one.
• Practice with a real 30-second clock, not a leisurely pace. The skill you're building is speed under pressure, and it doesn't transfer from untimed practice.

For that last one, a free countdown at countdownclockonline.com works well: set 30 seconds, label it "Numbers round," go full screen, and run it for every attempt. The 10 second countdown guide covers why a visible clock changes performance on short tasks.

The letters game: the rules exactly

Nine letters, at least four consonants and at least three vowels, thirty seconds, longest valid word wins.

• Letters are drawn one at a time from separate consonant and vowel piles, with the player calling each pick.
• The final nine must contain at least four consonants and at least three vowels.
• You have thirty seconds once the ninth letter is revealed.
• The word must appear in a standard dictionary. No proper nouns, no hyphenated words, no abbreviations.
• You score one point per letter, and a nine-letter word scores 18 rather than 9.
• Each letter may be used only as many times as it appears in the nine.

Vowel-heavy selections make short words easy and long words hard. Consonant-heavy selections do the reverse. Most experienced players ask for either three or four vowels and take the rest as consonants, which tends to produce workable seven-letter material.

How to solve the letters round by hand

Look for a suffix first, then see what stem the remaining letters make. Long words are almost always a shorter word plus an ending.

This is the single most productive habit in the letters game, and it's why experienced players find eight-letter words that beginners never see.

The endings worth scanning for, roughly in order of usefulness:

And the prefixes: RE-, UN-, IN-, DE-, DIS-, MIS-, PRE-, OVER-, OUT-.

The method:

1. Split the nine into vowels and consonants on paper. Seeing them separated breaks the visual pattern the letters were dealt in.
2. Check for -ING, -ERS, -IER and -ATE. If one is present, mentally set those letters aside.
3. Ask what the remaining letters spell. With four or five letters left, a stem is often obvious.
4. If no suffix is available, hunt for a strong consonant cluster — CH, SH, TH, ST, TR, BR, PL, CR — and build outward from it.
5. Always bank a safe word early. Find a five, write it down, and then reach for longer. Ending the round with nothing because you were chasing an eight is the classic mistake.

Two more techniques that genuinely help:

Rewrite the letters in a different order. Copy them out in a circle, or in reverse, or grouped by vowel and consonant. Your brain gets stuck on the order it first saw, and physically rearranging them breaks the fixation. This is the single most effective anagram trick there is.

Say the vowel skeleton. With E, A, I in hand, think about which vowel patterns real words use: _A_I_E_, _E_A_I__. Words have rhythm, and the vowel positions do most of the work.

How software solvers work, briefly

A numbers solver enumerates expression trees; a letters solver hashes a dictionary by sorted letters.

For the numbers game, a solver takes every pair of available values, applies each of the four operations, discards results that aren't positive integers, and recurses on the reduced set. Six numbers give a search space in the hundreds of thousands of expressions, small enough that a laptop finishes it in well under a second and can report the shortest solution, not just any solution.

For the letters game, the trick is that anagrams share a signature. Sort the letters of "listen" and you get eilnst; sort "silent" and you get the same. Store a dictionary keyed by those sorted signatures, then generate the subsets of your nine letters, sort each one, and look it up. No searching required.

Knowing this is mildly useful as a player, because it tells you what a solver is good for. It will always find the longest word, so it's a poor practice partner in the moment and an excellent one afterward. Attempt the round yourself under the clock, then check what was available. The words you missed are the vocabulary you're actually building.

Playing at home

You need slips of paper for the letters, a way to pick numbers, and a thirty-second timer. Nothing else.

A workable setup:

• Write the consonants on slips in rough proportion to English usage: plenty of R, S, T, L, N, D; only one each of J, Q, X, Z.
• Write vowels on separate slips, with A, E, I, O appearing more often than U.
• For numbers, use two sets of cards 1 to 10 plus single cards for 25, 50, 75 and 100.
• Generate the target by rolling or drawing digits, discarding anything under 101.
• Run a visible 30-second countdown that everyone can see, and stop hard at zero.

A round of nine letters, then six numbers, then repeat, makes a good fifteen-minute session. Scoring keeps it competitive, but the honest reason to play is that both puzzles are unusually well designed: short enough to stay sharp, hard enough to still surprise you after years.

Frequently asked questions

Is using a countdown solver cheating? Not if you use it after the round rather than during it. Solving under the clock and then checking what was possible is how people improve. Looking up the answer before the timer ends teaches you nothing except how to type quickly.

What's the hardest kind of numbers target? A large prime with an awkward remainder, particularly in the high 800s and 900s, when you've picked no large numbers. Primes can't be factored into a clean multiply-up, so you're forced into addition and subtraction chains, and small numbers don't reach far enough.

How many large numbers should I pick? One or two suits most players. Four large numbers gives you enormous reach but very little fine control, so you often land close and can't trim. Zero large numbers makes high targets genuinely hard. One large plus five small is the most flexible combination.

Can I use a number twice in the numbers round? Only if it was dealt twice. The small pool contains two of each value, so a set could legitimately include two 7s. Otherwise every number is used at most once.

Are plurals and verb forms allowed in the letters round? Yes, as long as the form appears in the dictionary. That's exactly why the suffix-first method works so well: -S, -ED, -ING and -ERS turn a six into a nine surprisingly often.

How long should I practice for? Short and frequent beats long and occasional. Six rounds a day under a real timer will move you further in a month than an hour once a week. Use the same thirty-second clock every time so the pressure feels identical, and the 2 minute countdown guide covers why a visible timer changes how people perform on timed work.