NumGrid strategy guide
NumGrid rewards arithmetic deduction more than guessing. The digit-sum hint alone eliminates 90–99% of the 100,000 possible 5-digit numbers before you make a single guess. Players who consistently solve in 3–4 guesses are doing the math, not just throwing digits at the grid.
The math before the first guess
The number of 5-digit combinations is 100,000 (00000–99999). The digit-sum hint narrows this dramatically:
- Sum = 0: exactly 1 combination (00000) — but trivial puzzles are excluded.
- Sum = 1: 5 combinations.
- Sum = 22 (median): about 6,800 combinations.
- Sum = 45: exactly 1 combination (99999) — also excluded.
The parity hint then cuts the remaining set roughly in half. After both hints you’re usually looking at 2,000–3,500 candidates, not 100,000.
Opener strategy
Your first guess should do two things: cover unfamiliar digits AND test the sum/parity constraints. Three classes of opener work well depending on the sum hint:
- Low sum (0–15): the digits are mostly 0, 1, 2, 3. Open with something like
01234(or a permutation that respects parity). You will get many greens or yellows and learn which low digits are in. - Mid sum (16–29): the digits are spread. Open with a digit-diverse number like
13579(covers all odd digits) or02468(covers all even digits). Pick based on parity hint. - High sum (30–45): the digits are mostly 7, 8, 9. Open with
56789or89876(variant; covers high digits).
Using the parity hint
Parity tells you about the LAST digit. If the puzzle is even, the last digit is one of 0 2 4 6 8. If odd, one of 1 3 5 7 9. This collapses 5 of the 10 possible last digits — equivalent to half a free guess on position 5.
Tactical use: don’t waste your opener guessing an even last digit if the puzzle is odd. Put a digit there that matches parity so you can immediately distinguish “in the number” from “in the right position.”
The deduction loop
- After each guess, recompute the sum constraint with the locked digits. If position 1 is locked at 7 and digits sum to 18, the remaining 4 digits sum to 11.
- Use yellow digits aggressively. A yellow tells you a digit is IN the number — pick your next guess to test where.
- Eliminate. Each gray digit removes 1/10th of the candidate space on average.
The doubled-digit trap
About 40% of NumGrid puzzles contain a doubled digit (e.g. 25525). Newer players often assume yellow means “that digit appears once” — but if the answer has two of a digit and you guess two of it, both can light up. Conversely, if you guess two and only one shows yellow, the answer has only one. Watch for this in puzzles where your digit sum is divisible by something easy (sum 20 with two 5s is more likely than sum 21 with two 5s, for example).
Endgame: the last 1-2 guesses
When you’re down to 1-2 guesses, write out the constraints explicitly:
- What digits are confirmed IN (greens + yellows)?
- What positions are locked (greens)?
- What does the remaining sum need to be?
- What does parity say about the last digit?
If the constraints leave 2-3 candidates, pick the one that most matches common digit patterns (avoid lots of zeros unless you have a clue they’re there).
Pace and practice
The fastest players take 30–60 seconds total: 10 seconds to do the sum math, 5 seconds per guess, plus thinking time. Don’t rush — the puzzle rewards 30 seconds of careful constraint analysis more than 6 hasty guesses.
New to NumGrid? Start with the rules.