There is a better way to handle this. The manual cross-referencing that has been passed down with this spreadsheet is exactly the kind of repetitive, error-prone work that modern tools can eliminate.
What you are describing is not only possible, it is a textbook use case for conditional formatting and basic lookup functions. Excel already has the logic built in to scan your old lists and flag overlaps the moment they are entered. The key is to stop thinking of this as a puzzle to solve each month and start thinking of it as a pattern to automate. The verbiage you need to search for is "COUNTIF" and "conditional formatting." COUNTIF tells Excel to count how many times a specific number appears across a range of cells. If the count is greater than one, you have an overlap. Conditional formatting is the tool that makes that overlap visible instantly, turning the cell red or highlighting it so you never miss it. Together, they turn your manual check into an automatic safeguard.
The practical first step is small. Create a new sheet in your existing workbook that compiles all the numbered ranges from previous months into a single column. Then, on your new monthly assignment sheet, apply a conditional formatting rule using COUNTIF. The formula looks like this: =COUNTIF(OldRanges, A1)>0. Replace "OldRanges" with the actual range of your compiled list, and "A1" with the first cell of your new assignments. When you type a number that has been used before, the cell changes color. No manual scanning. No second-guessing. For populating a new list without overlap, you can take it further with a helper column that generates available numbers using the SMALL and IF functions in an array formula, but the highlighting approach is where you start.
What makes this worth doing is not the time saved on one task. It is the confidence that comes from knowing the system catches errors before you do. The person who built this manual process was solving the problem with the tools they had. You have better tools now. Take the hour to learn these two functions, and you will never need to cross-reference a list again. That is the kind of small investment that pays back in every monthly cycle to come.