Parity Strategy

Parity is the underrated NumGrid hint. The digit sum gets all the attention because it collapses the candidate set so visibly, but parity quietly does just as much work — it halves whatever remains and it pins down the most important position in the puzzle.

What parity actually constrains

A number is even if its last digit is 0, 2, 4, 6, or 8. It is odd if its last digit is 1, 3, 5, 7, or 9. The first four digits have no effect on the number’s parity.

So the parity hint, technically, is a hint about position 5 only. It divides the ten possible digits into two five-digit sets and tells you which set the last digit lives in. That sounds modest, but it accomplishes three things:

It halves the post-digit-sum candidate set.
It lets you choose an opener whose last digit is informative.
It interacts with the digit-sum residual to constrain the first four positions.

How to use it on the opener

Your opener’s last digit should match the day’s parity. If parity is even, end your opener in an even digit so the position-5 feedback tells you something useful. A guess ending in 9 against an even-parity day will always return gray (or yellow if 9 lives elsewhere) for position 5 — that is wasted feedback.

Recommended openers by parity:

Even days: 02468, 14792, 67890
Odd days: 13579, 14793, 56789

The parity + sum interaction

The two hints constrain different things, but their combination is multiplicative.

Example A: sum 22, parity even. The last digit is in {0, 2, 4, 6, 8}. The other four digits sum to 22 − (last digit). If the last digit is 0, the front four sum to 22. If 8, they sum to 14. Each combination has a different candidate count, but the parity hint cuts each possibility roughly in half.

Example B: sum 30, parity odd. The last digit is odd, so it’s in {1, 3, 5, 7, 9}. The front four sum to 30 − (last digit), which ranges from 21 (if last = 9) to 29 (if last = 1). Front-sum 29 forces four digits averaging 7.25 — so mostly 7s, 8s, and 9s. Front-sum 21 leaves more flexibility.

Using parity to constrain yellow digits

When you see a yellow digit on position 5, parity tells you something the feedback does not: that yellow can move to positions 1, 2, 3, or 4 — but it cannot stay in position 5 if its parity disagrees with the hint. This sometimes lets you place a yellow with confidence on turn 2.

Conversely, a yellow that does match the day’s parity remains a strong candidate for position 5 — especially if the residual sum forces a digit in that range.

Why position 5 is the anchor

Of the five positions, position 5 is the only one with a free hint. Lock it first if you can. Once position 5 is green, the remaining four positions become a smaller puzzle: 10,000 candidates from the start, narrowed by the residual digit sum to a few hundred, and narrowed further by every previous gray and yellow. Most NumGrid solves go through a turn-2 or turn-3 position-5 lock.

FAQ

What does the parity hint in NumGrid actually mean?

Parity refers to whether the whole 5-digit number is odd or even. A number is even if its last digit is 0, 2, 4, 6, or 8 — and odd if its last digit is 1, 3, 5, 7, or 9. The other four digits do not affect parity. So the parity hint is really a hint about position 5 only: it tells you which of two five-digit sets the last digit belongs to.

Why is the parity hint useful if it only constrains one position?

Because halving the search space matters a lot. After the digit-sum hint narrows you to ~2,000 candidates, parity halves it to ~1,000. More importantly, knowing the last-digit set lets you choose an opener whose own last digit matches — so the green/yellow/gray feedback on position 5 is informative rather than wasted.

Can the parity and digit-sum hints contradict each other?

No, they are always consistent — the puzzle picks a real answer and shows both hints derived from it. But they can interact in useful ways. For example, sum 25 with parity "even" means the last digit is even (sum 0, 2, 4, 6, 8) and the other four digits sum to 25 minus that even number. A sum of 25 and an even last digit of 0 means the other four digits must sum to 25 — a tall ask that forces multiple large digits in the first four positions.

Are odd-parity puzzles harder than even-parity puzzles?

Marginally. Odd parity gives slightly more candidates because odd-last-digit numbers have a wider distribution of small-digit prefixes. The difference is statistically tiny — about 1-2% — and far smaller than the variation introduced by where the digit sum falls. Parity does not drive day-to-day difficulty.

Lock position 5 first on today’s puzzle — play today’s NumGrid puzzle →