How to solve NumGrid in 3 guesses

The 3-guess solve is the NumGrid equivalent of a hole-in-one. It requires combining the two free hints (digit sum + parity) with disciplined opener selection. Players who do this consistently are using six pieces of information per guess — five per-digit feedback plus the sum/parity reconciliation — to narrow 100,000 candidates to under 10 by guess 2.

The math: how 3 guesses can suffice

NumGrid’s search space starts at 100,000 (00000-99999). The digit-sum hint reduces it to typically 2,000-7,000 candidates. The parity hint halves that to roughly 1,000-3,500. A well-chosen opener with 5 distinct digits typically returns 4-5 information-bearing feedback cells, eliminating ~80% of remaining candidates. After two guesses, you’re usually down to 5-15 candidates — easily solved on guess 3.

The 6 steps

Step 1: Read both free hints carefully

Before your first guess, write down the digit sum and parity on paper or in a notes app. Sum 8 with even parity is very different from sum 22 with odd parity — they imply different candidate sets.

Step 2: Compute the candidate space

Use the digit sum to estimate roughly how many 5-digit combinations satisfy it. Sum 8 has ~700 combinations; sum 22 has ~6,800. Parity halves whichever number you get. Knowing the size of the haystack tells you how aggressive to be.

Step 3: Pick a high-information opener that respects parity

Your opener should test 5 distinct digits AND end with a digit that matches the puzzle's parity. Good opener for sum 8 + even: 10260 (digit sum 9 — close but not exact, tests 5 unique digits, even). Good opener for sum 22 + odd: 14761 (sum 19 — close to 22, ends odd, 5 distinct digits).

Step 4: After guess 1, eliminate aggressively

Each gray digit cuts the candidate space by ~9% on average. Two greens cut it by ~90%. Track which digits are IN (yellow/green) and which are OUT (gray) — write them down.

Step 5: Guess 2: lock positions of confirmed digits

For your second guess, place each in-digit at a position you haven't tested yet. If 4 went yellow in position 2, try it in position 4. The goal is to convert yellows to greens or eliminate positions.

Step 6: Guess 3: solve from constraints

By guess 3 you should have 3-5 cells locked. Write out the constraints: confirmed digits, positions, remaining sum, parity. There should be only 1-3 candidates. Pick the most arithmetically likely.

Worked example

Puzzle: digit sum 18, odd.

Opener: 35719 (sum 25 — too high; better choice: 12347, sum 17, ends odd). Suppose result: 12347. Position 2 = 2 (green), position 5 = 7 (green), digit 3 is in (yellow). Remaining 3 cells must sum to 18 - 2 - 7 = 9. Confirmed digits: 2, 7, 3. Last cell (position 5) is 7, but position 5 must be odd to match parity — 7 is odd, consistent.

Guess 2: place 3 at a new position; pick remaining digits to test. Try 32796: sum 27 — no, must equal 18. Try 32709: sum 21 — closer but still wrong. Try 32700 — sum 12, too low. Try 32907 — sum 21. We need sum 18 with confirmed 2 in pos 2 and 7 in pos 5, plus 3 somewhere. Try 02307: 0 + 2 + 3 + 0 + 7 = 12 — too low. Better: 32196 — sum 21 — no. Try 92307: 9+2+3+0+7 = 21 — too high. Try 32157: 3+2+1+5+7 = 18 ✓ ends odd ✓ — submit.

Suppose result: 32157. Locked: 3, 2, _, _, 7. 5 is in (yellow). Remaining 2 cells must sum to 6 with 5 in one of them. So one cell is 5 and the other sums to 1 → must be 1 or 0. We tested 1 in position 3 → gray; so position 3 is NOT 1.

Guess 3: try 32567 (sum 23 — no). The remaining cell pair sums to 6, contains a 5, and the non-5 is 0 or 1. Since 1 in position 3 was gray, try 5 in position 3. That means position 4 has digit summing to 1 → could be 1 (but only if position is not 3). Try 32517: 3+2+5+1+7 = 18 ✓. Submit. WIN.

Common 3-guess mistakes

Ignoring parity on guess 1. If parity is odd, your opener’s last digit must be odd. Wasting a guess on an even last digit when parity is odd costs you a full guess of position-5 information.
Not adjusting opener to the sum bucket. Sum 8 vs sum 30 demand completely different openers (low digits vs high digits).
Failing to write down constraints. Mental constraint-tracking past guess 2 is hard; a notepad triples your success rate.

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