A number-fit crossword on a 6x6 grid. Each run of connected blanks takes one number, a digit per cell, and the run length must equal that number's digit count. Where an across run and a down run share a cell they must agree. The middle row already shows 4, 5, 3. Place all twelve numbers.
Your answer
Watch outA run of the right length is tempting, but every crossing digit has to agree — one clash undoes the whole run.
How to solve
StrategyEliminate Possibilities — The pool of numbers for each run length is small and finite, so I use the fixed digits (the given 453 and each crossing) to eliminate every number that does not fit a run, narrowing each run to one choice. The grid itself is the diagram that records the crossing digits as I lock them in.
1STEP 1
Place the two-digit numbers using the given 453
Only one two-digit number starts with 3, so 34 and 27 fall out at once.
3□ → 34, other 2-digit = 27
A two-digit number's leading digit fixes which number it can be; once one is forced, the other two-digit number has only one home left.
2.NBT.A.1Eliminate Possibilities
Once the leading digit forces one two-digit number into its run, the other two-digit number has only one run left to go in.
Why?
A run's first cell is its leading digit, and a number can only sit in a run whose leading digit it matches.
🧱Place-value groupingTen ones make one ten and ten tens make one hundred — each place bundles ten of the last.
Why?
With one of the two runs taken and only two two-digit numbers to place, the remaining number has nowhere else to go.
🧱Rule out the rest and the last one is forcedIf every possibility but one has been ruled out, the survivor must be the answer — no further checking is needed.
2STEP 2
Lock the three-digit runs through the 4 and the bottom 27
The down run from the 4 meeting that 2 is 402, and the middle across run is 453.
4□2 → 402
Knowing the hundreds and ones digits of a three-digit run usually pins it to exactly one of the listed numbers.
2.NBT.A.1Eliminate Possibilities
3STEP 3
Use the 5 to fix the first four-digit number
Just one four-digit number ends in 5, so that down run is 6715.
□□□5 → 6715
Matching a single known end digit against four candidates leaves just one possibility for a four-digit run.
4.NBT.A.2Eliminate Possibilities
4STEP 4
Finish the four-digit runs by their crossings
Crossing that 7 and a 0 fills 4070, 4630, 3069 in turn.
□□7□ → 4070, □□□0 → 4630, last → 3069
Each new crossing digit removes candidates until exactly one four-digit number fits each remaining run, and the shared cells all stay consistent.
4.NBT.A.2Guess And Check
5STEP 5
Fill the last three-digit runs
The leftover three-digit numbers land as 646, 536, 326, 325.
□4□ → 646, □36 → 536, □□6 → 326, 3□5 → 325
With the crossing digits known, each three-digit run has a unique match, and every shared cell agrees - the whole grid clicks into place.
2.NBT.A.1Eliminate Possibilities
Answer
across 326, 4070, 536, 453, 4630, 27 / down 325, 3069, 646, 402, 6715, 34
Every run length matches the digit count of the number placed (two 2-runs, six 3-runs, four 4-runs), all twelve listed numbers are used exactly once, and every crossing digit agrees (e.g. the shared 6 between 4630 and 3069, the 7 between 6715 and 4070, the 3 between 453 and 34). The given 4, 5, 3 in row 4 is preserved.
Takeaway
Start from the digits you already know - each fixed digit crosses out choices until only one number fits each slot!
Place the two-digit numbers using the given 453
Lock the three-digit runs through the 4 and the bottom 27