Countdown Numbers Solver 2026: Step-by-Step for Any Target

November 8, 2026 · 6 min read

Six numbers, one target, thirty seconds. The clock is the whole problem. Solving under that pressure needs a fixed procedure, not a hunt across 15 billion possible expressions. The routine below handles every legal board of four operators and six integers, and it fits inside the Countdown clock. Each worked example runs on real tile distributions from broadcast episodes and solver databases, with the exact sequence of operations the greedy path finds first.

The Greedy Algorithm In Four Passes

The greedy routine walks four passes over the six tiles. Pass one looks for a multiplication that lands within 10% of the target: with target 742 and a tileset including 75 and 10, you take 75 x 10 = 750 and park an 8-point gap. Pass two folds in a second tile to close most of that gap through addition or subtraction, so 750 minus an 8-tile delivers 742 in one move. Pass three uses the remaining tiles to generate any residual through combination, often two small tiles summed, subtracted, or divided to hit the exact delta. Pass four confirms the write-up follows legal Countdown order: no fractions at intermediate steps, no negative intermediates, no reusing a tile. The whole sequence runs in 14 to 22 seconds once drilled to automaticity.

Anchor the first multiplication with the nearest large-tile product. Large tiles are 25, 50, 75, 100, and their products with any small tile run from 25 up to 1000. A target of 437 pairs cleanly with 50 x 9 = 450 or 75 x 6 = 450, leaving a 13-point residual that two small tiles can almost always generate. A target of 952 wants 100 x a built 10 plus a small adjustment, or 75 x 13 constructed from a 10 and a 3. The anchor halves your search from a 6-tile combination problem to a 4-tile residual puzzle, and a 4-tile residual is where mental math wins. Readers new to the round can get the broadcast rules and point values from our full guide to the mechanics.

Ten Worked Boards From Easy To Nasty

Each board below lists the six tiles, the target, and the exact expression the greedy pass finds first. Unused tiles are legal and common: Countdown rules do not require consuming every tile, only that the expression evaluates to the target with no reuse and no illegal intermediate value.

1. Tiles 100, 75, 2, 3, 6, 8, target 439: 75 x 6 - 8 - 3 = 439. Pass-one anchor is 75 x 6 = 450, residual 11 built as 8 + 3.
2. Tiles 50, 25, 1, 4, 7, 9, target 384: 50 x 7 + 25 + 9 = 384. Anchor 50 x 7 = 350, residual 34 built as 25 + 9.
3. Tiles 100, 50, 5, 8, 2, 10, target 568: 100 x 5 + 50 + 10 + 8 = 568. Residual 68 built from three small additions.
4. Tiles 75, 25, 3, 6, 7, 2, target 593: (75 + 25) x 6 - 7 = 593. Large-tile sum times a small tile, residual 7 is a single tile.
5. Tiles 100, 50, 25, 4, 5, 6, target 729: 100 x 6 + 25 x 5 + 4 = 729. Two multiplications stacked because neither alone closes the gap.
6. Tiles 75, 50, 10, 8, 4, 1, target 821: 75 x (10 + 1) - 4 = 821. The multiplier is built from two small tiles before the main multiply.
7. Tiles 100, 25, 7, 6, 5, 2, target 683: 100 x 7 - 25 + 6 + 2 = 683. Anchor overshoots by 17, residual built from the 25 and two smalls.
8. Tiles 50, 9, 7, 6, 4, 2, target 466: 50 x 9 + 7 x 2 + 6 - 4 = 466. Mixed residual uses a secondary multiply and two single tiles.
9. Tiles 100, 50, 10, 7, 6, 3, target 846: 100 x 7 + 50 x 3 - 10 + 6 = 846. Two anchors stack because the gap is 146.
10. Tiles 75, 50, 25, 10, 4, 3, target 540: 75 x (4 + 3) + 25 - 10 = 540. Built multiplier plus trimmed residual.

Five Shortcuts That Beat Pure Search

A brute-force search of all 6-tile expressions touches roughly 33 million legal forms before pruning. Five shortcuts cut that to under 200 candidates, which fits inside working memory. Each shortcut removes one dimension of the search tree and compresses pass-one recall.

• Round the target to the nearest 25. A target of 437 becomes 425 or 450, both reachable by a large-tile product, and the residual search drops to under 25.
• Lock in the dominant large tile. One of 75 or 100 appears in the final expression for targets above 400 roughly 85% of the time. Build the anchor around it before examining the smalls.
• Pre-compute the four key product tables: 25 x small, 50 x small, 75 x small, 100 x small. Those 40 products cover every legal pass-one anchor.
• Keep a 1-tile uncommitted. A single 1 held in reserve gives a cheap final correction when the residual is off by a single point.
• Check divisibility of the target by 25, 50, and 75 in the first two seconds. A target of 675 is 75 x 9 outright; no residual work needed.

When Greedy Misses And How To Score The Close One

Greedy fails on prime targets stranded between large-tile products and on tilesets heavy with ones. A target of 719 with tiles 75, 50, 25, 9, 2, 1 has no exact expression: 75 x 9 + 50 lands 725, 75 x 9 + 25 + 19 collapses, and every residual path sits within 5 of the target but not on it. The competition rule awards 7 points for landing within 10 and 5 points for within 5, so the second-best answer still banks most of the available credit.

Switch modes the moment pass three fails to zero out the residual. Take the closest reachable integer, write it down, and move on. A 7-point partial beats a 0-point empty answer, and the clock punishes hesitation more than approximation. The deeper mechanics of partial scoring and tie-breaking rules sit inside our full solving strategy piece. A side-by-side with the 24 Game format appears in our target-number puzzle breakdown for readers comparing the two clocks.

A 14-Day Drill To Hit Thirty Seconds

The drill splits across two weeks. Week one builds the 40-product anchor table from memory and runs easy boards at 60 seconds. Week two tightens the clock to 30 seconds and adds nasty boards with prime targets and awkward small-tile distributions. Twenty boards a day for 14 days lands the average solver under 30 seconds on 70% of boards. The scheduling and board generation live inside our daily practice rotation, which serves a fresh target every day at midnight local time.

Score every attempt on the Countdown rubric: 10 for exact, 7 for within 5, 5 for within 10, 0 otherwise. Track per-category scores by day. Expect week-one averages near 4 points per board and week-two averages near 7. If the week-two score plateaus below 6, the bottleneck is pass-one anchor recall, not residual computation; drill the 40-product table from scratch before adding more boards.

Pair the solo drill with timed head-to-head rounds against another solver or against a solver bot. Competitive pressure compresses the pass sequence and surfaces the tiles your brain skips under load. Logging the bot's path after each round reveals the second and third anchors you missed, which widens the search tree inside your head over time without adding memory load.