Summary: A Number Fill — also called a number fit or number fill-in — is a crossword-style grid with no clues and no words. You get an empty grid, the full list of numbers sorted by length, and a few starter digits already printed; fit every number into the grid so the across and down entries agree where they cross. This guide covers the rules, where to start, and a worked example from the starter digits.
Overview
Picture a crossword grid where every entry is a number instead of a word. Under the grid sits the list: every three-digit number, every four-digit number, and so on, sorted into groups. A handful of single digits are printed in the grid to start you off. Your job is to put every number back where it belongs.
The same puzzle twice: as it prints, with four starter digits in place, and solved. The list under the grid holds every number in the grid, grouped by digit count.
There is no vocabulary to know and nothing to spell. Length tells you which slots a number can go in, and the digits where entries cross tell you which slot it does go in. It plays the same in any language, which is why number fits travel so well.
The Goal
Write every number from the list into the grid, one number per slot, so that every across entry and every down entry is a number from the list and the digits agree wherever two entries cross. When the last number is placed, the grid is full and the list is used up.
Number Fill Puzzle Rules
- Every listed number is used exactly once. The list is complete: nothing missing, nothing extra. Tick numbers off as you place them.
- A number only fits a slot of its own length. Count the cells in a slot, then look only in the group with that many digits.
- Crossings must agree. Every white cell belongs to an across entry and a down entry, and the two share that digit. Two different digits in one cell means a placement is wrong.
- No number repeats, and none starts with 0. Each number appears once in the list and once in the grid, and the first digit of every entry is 1 to 9 — so a slot whose first cell you know is 0 cannot be the start of anything.
- The starter digits are single cells. A few digits are printed before you begin. Every white cell belongs to an across entry and a down entry, so one printed digit fixes a digit in two entries at once: four starters open eight entries.
- The digits carry no meaning. Nothing to calculate — only positions to match.
How to Solve a Number Fill, Step by Step
The steps below are worked on a 9 × 9 puzzle, shown here with its list. Its four starter digits are an 8 in the fourth row (the last white cell before the black squares), a 2 in the seventh row, a 5 in the eighth and a 9 in the bottom row.
A short board: two six-digit numbers, two four-digit numbers, ten five-digit numbers and eighteen three-digit numbers to place.
- Start at a starter digit in a long slot. The 8 in the fourth row is the last cell of a six-cell across slot. Only two six-digit numbers are in the list, and only one of them — 126508 — ends in 8. Write it in: six cells filled from one printed digit.
- Follow the new digits into the slots they cross. The 1 that begins 126508 is the bottom cell of a four-cell down slot. There are two four-digit numbers, and only 5791 ends in 1, so that is the down entry — and the other four-digit number, 1935, must go in the only other four-cell slot on the board.
- Let a placed digit open the slot below it. The 5 fourth along in 126508 is the top cell of a five-cell down slot. Only one five-digit number starts with 5 — 51520 — and the starter 2 in row seven, sitting in that slot’s fourth cell, confirms it before you write a digit. An inside starter earns its keep when two candidates share a first digit: then it is the tie-breaker.
- Count the candidates, then check the crossings. When a slot has two or three possible numbers, look at the cells you have already fixed. The starter 5 in row eight begins a three-cell entry, and the three-digit group has three numbers starting with 5: 513, 517 and 589. The down entry through the second cell puts a 1 there, which rules out 589, and the 3 that 1935 already put in the last cell settles it: 513.
- Rule out leading zeros. Before you write a candidate in, check where its zeros land: if one would fall in the first cell of a crossing entry, that candidate is out, because no listed number starts with 0.
- Finish from the list. Late in the solve, the numbers still unticked are the numbers still unplaced, and by then each one has a slot or two left of its length. Match them and the grid closes.
Word Fill: the Same Puzzle with Words
Number Fill has a sibling that plays by the identical rules with words instead of digits: Word Fill. There the list is words grouped by length and a whole word is revealed as the starter. See How Word Fill Puzzles Work.
Try It Online
Play Number Fill in your browser. Click a square and type a digit on the keypad, or drag a number from the list straight onto a slot of the right length — the digits drop in, and a number that would clash with a starter simply refuses the slot. Press Check to test the whole grid when you think you are done. The general player controls — checking, resetting, the timer, working through a set — are covered once in How to Play Puzzles Online.
Outcome
You now know what a Number Fill asks of you — place every listed number so the grid interlocks — and how it opens: start at a starter digit in a long slot, follow the new digits into the entries they cross, use starters that sit inside longer slots, and close the last few numbers from the list. Want to make your own? See How to Create Number Fill Puzzles in Puzzle Maker Pro, or try the free demo first.
FAQ
Do the numbers mean anything?
No. The digits are just digits — nothing to add up or continue. You place the numbers by length and by the digits where entries cross.
Is a Number Fill the same as a Kakuro or a Cross Sum?
No. Those give you totals and ask you to work out the digits. A Number Fill gives you every number already and asks you to fit them into the grid.
Why are the starters single digits rather than a whole number?
A single printed digit sits at a crossing, so it fixes one digit for two entries at once. A few of those scattered across the grid open more of the board than one whole number would.
Where do I start?
At a starter digit that sits in one of the longest slots. There are only a few long numbers in the list, so the one that matches the starter’s position is usually obvious, and placing it fills several cells at once.
Do I ever have to guess?
Rarely. Work from the placements with a single candidate — a starter in a long slot, then the entries it crosses — and each new digit narrows the next slot. If two candidates remain, pencil one in; the next crossing either confirms it or tells you to swap.