Digit Sum Strategy
The digit sum is the most powerful single piece of information in NumGrid. It eliminates 97-99% of the candidate space before your first guess, and when used correctly during play it can collapse your candidate set to single digits by turn 2.
What the digit sum tells you
The digit sum is the sum of all five digits in the hidden number. It ranges from 0 (00000) to 45 (99999). Most days the sum sits between 15 and 32. Every puzzle reveals it for free, at the top of the board, before you guess.
The candidate distribution
Not every sum is equally common among 5-digit numbers. The distribution is bell-shaped, peaking around sum 22-23. A rough table:
| Sum | Candidate count (approx.) | Difficulty |
|---|---|---|
| 5 | 126 | Easy |
| 10 | 1,001 | Moderate |
| 15 | 2,247 | Moderate |
| 22 | 3,490 | Hardest |
| 30 | 1,751 | Moderate |
| 35 | 756 | Moderate |
| 40 | 126 | Easy |
The hardest days are the ones with middle sums (20-25), because the candidate set is largest. The easiest days are the tail-end sums (under 10 or over 38), where you may have only a hundred or so candidates from the hint alone.
The residual-sum technique
This is the highest-leverage tactic in NumGrid. After your first guess, compute the residual sum: the puzzle’s sum hint minus every confirmed digit (green or yellow).
Example. The puzzle’s sum is 19. You guess 13579 and get: 1 = gray, 3 = yellow, 5 = green-pos-3, 7 = gray, 9 = yellow.
Confirmed digits: 3, 5, 9. Their sum is 17. The residual is 19 − 17 = 2. The two remaining unknown positions must hold two digits summing to 2. Valid pairs: (0, 2), (2, 0), (1, 1) — but 1 was grayed, so (1, 1) is out. Realistic candidates: (0, 2), (2, 0).
You now have only a handful of valid candidate numbers (5 _ _ with 3, 9 somewhere and 0, 2 in the remaining slots). Your second guess can lock the answer.
When the residual is impossible
If your residual is negative (impossible — you over-counted yellows for a digit that only appears once in the answer) or larger than what the remaining slots can hold (max is 9 per slot), you have misread the feedback. The most common cause is forgetting that a yellow + a gray for the same digit means “exactly one”, not “at least one and not the other”.
Choosing the opener by sum
The opener’s sum should sit close to the day’s sum. Why? An opener of 01234 (sum 10) tested against a day with sum 38 will return mostly grays — almost none of those small digits are in the answer. That is wasted information. An opener whose sum is within ±5 of the day’s sum is much more likely to return useful greens and yellows.
FAQ
What is the digit sum in NumGrid?
The digit sum is the sum of all five digits in the hidden number. The minimum is 0 (the number 00000) and the maximum is 45 (the number 99999). Every NumGrid puzzle shows you this number for free, before you guess. It is one of two free hints — the other is parity.
How much does the digit sum hint narrow the candidates?
It typically eliminates 97-99% of the 100,000 candidate numbers. The distribution is bell-shaped, peaking around sum 22-23 (about 3,490 candidates) and dropping to tens or single digits at the extremes (sum 0 has exactly 1 candidate, sum 45 has exactly 1). Combined with parity, the post-hint candidate set is usually 400-1,800 numbers.
How do I "use" the digit sum during a guess?
After every guess, recompute the residual sum: take the puzzle's sum hint and subtract every digit you have confirmed as green or yellow. The remaining digits in your candidate answer must sum to that residual. This often forces specific digits into specific slots — especially when the residual is small (forces small digits) or large (forces large digits).
What does it mean if the digit sum is 0 or 45?
The puzzle is trivial — sum 0 means the answer is 00000, sum 45 means the answer is 99999. NumGrid excludes these and other "trivial" cases from the daily puzzle pool, so the lowest sums you will actually see are around 5 and the highest around 40.
Apply the residual-sum technique on today’s puzzle — play today’s NumGrid puzzle →
See also: parity strategy, best openers, and the rules.