Replacing cogs for shimano 105 7 speed.

On behalf of a friend here is the problem.

For a Trek 2100 with a shimano 105 hyperglide 7 speed there is the need for a custom cassette with these desired gears

21,20,19,18,17,?,?

The 2 questionmarks are left open as it's not important what number they contain as the upper numbers are more important.

Now the problem is that the stock shimi cassette is 13,14,15,16,17,19,21.

Also the replacement cogs are all from the latest models (thinner) so would there for be the best solution to buy a 9/10 speed cassette and just remove/replace what's not needed use the correct spacers and go from there to obtain the desired cassette.

What is the solution please let us know.

The outer cog would have to be a 12 or 13 (the outer cog is different from others), so I'd suggest 13-15 for the last 2 positions. Many Shimano cassettes come with some or most of the cogs attached together on a carrier, so you can't plan on buying a prebuilt cassette and swapping around any cogs you want. Read Sheldon's Brown cassette writeup and it should tell you what you need to know.

Thanks a lot for the link.

I'm sure my friend will be helped by this.