THE RULES — QUICK REFERENCE
Six source numbers: typically one to four large numbers (25, 50, 75, 100) plus small numbers (1–10). A 3-digit target between 100 and 999. Use any subset, each number at most once, with +, −, ×, ÷. All intermediate results must be whole numbers and positive. Exact = full points. Within 10 = partial. More than 10 away = nothing.
STEP 1 — LARGE × SMALL SCAN (FIRST 10 SECONDS)
The single most useful first move: multiply each large number by each small number and check the result against the target.
Target 954 · numbers: 100 · 75 · 25 · 9 · 4 · 3
100 × 9 = 900 → 54 away. Remaining: {75, 25, 4, 3}.
75 − 25 + 4 = 54 ✓ → 100 × 9 + 75 − 25 + 4 = 954
That took two lines. The key observation: 900 is close to 954, so pause there, compute the gap (54), then check whether the remaining numbers cover it — often one or two small numbers do the job immediately.
In practice this scan takes 5–10 seconds. If any large × small product is within 20 of the target, pause there and check whether the gap is coverable by the remaining numbers. If yes, declare.
STEP 2 — ROUND-NUMBER PROXIMITY (SECONDS 10–15)
Check whether the target is close to a round multiple: 100, 200, 300, 400, 500, 600, 700, 800, 900, or a multiple of 25 (125, 150, 175, …).
If yes: can you reach that round multiple exactly from your numbers? Then the remaining gap is small and easily closed.
- Target 497: 500 − 3. Can you make 500? 100 × 5, or 50 × 10. Then 500 − 3 if you have a 3.
- Target 756: 750 + 6 = 75 × 10 + 6. Or 25 × 30 + 6 = 25 × (3 × 10) + 6.
- Target 624: 600 + 24. 100 × 6 + 24. Do you have 6? If not, 100 × (6...) — check other routes.
STEP 3 — (LARGE × a) ± SMALL FINE-TUNING
Most solvable Countdown targets follow this template: a large number (or product of a large + small) gets you within 10–20, then one or two small numbers close the gap.
Work through these systematically: for each large number L, compute L × 2, L × 3, … L × 9 (multiplying by each small number you have). Note the gap from each product to the target. If the gap equals a sum or difference of the remaining small numbers, you have a solution.
Target 648 · numbers: 100 · 50 · 25 · 8 · 4 · 2
100 × 6 = 600 → gap = 48. Remaining: {50, 25, 8, 4, 2}.
50 − 4 + 2 = 48 ✓ → 100 × 6 + 50 − 4 + 2 = 648
STEP 4 — DECLARE A NEAR-MISS IF EXACT FEELS FAR (SECOND 20+)
If exact hasn't appeared by the 20-second mark, pivot to finding a near-miss within 10.
The fastest near-miss: take the best product from your step-1 scan and check how many small numbers away from the target you are. A difference of 1–9 that you can reach exactly with remaining numbers is worth declaring — partial points beat zero.
Keep the near-miss in your back pocket even while looking for exact. The moment you have a valid declaration within 10, note it — you can always upgrade to exact if you find it with time remaining.
THE SOLVING ORDER
- Scan large × small products for anything within 20 of the target.
- Check round-number proximity (nearest 100, nearest 25-multiple).
- For promising products, check if remaining numbers close the gap exactly.
- If within 10 of the target with any combination, hold that as your declaration.
- After ~20 seconds without exact: commit to the best near-miss and keep checking for exact.
THE BEGINNER TRAP
Adding small numbers together first. 3 + 4 + 7 + 8 = 22 — now what? You've used four numbers and produced something that doesn't helpfully relate to a three-digit target. The large numbers are the only way to get into the right range quickly. Small numbers are for fine-tuning, not construction.
A good mental rule: never use a small number until you have a large-number base to adjust. The large number gets you to the right hundreds. A small number moves you the last few digits.