How many letter tiles does one need to build any 24 word mnemonic? One of the popular cold storage wallets provides double-sided tiles for users to put in the first four letters of each of their 24 words (96 characters total).

They include ~245 double sided tiles, plus some blanks.

By my math on the BIP39 wordlist, they should need to provide ~485 double sided tiles to provide for every valid 24 word mnemonic.

I simply calculated, for each letter, the worst case 24 word combination, then added up how many of each letter I would need, then divided by 2 since the tiles are double sided.

Is there something I'm missing here?

Thanks!

EDIT  I have found at least one flaw in my reasoning. The last word is a checksum, so not entirely random. But accounting for this only saves us 33 letter tiles!
Actually the answer is rather simple, Cryptosteel did a letter frequency analysis on the bip39 wordlist and found that you can represent any word in the list using only 4 characters. Therefore, for a 24 word recovery phrase, you take 4x24 or 96 characters.

Edit: Oh oops, I thought the question was that ability to store all combinations instead of the tiles provided. to which my answer is, they probably ran an analysis and decided on that number of tiles based on their data. If it bothers you, you can just use a cold wallet that includes more tiles like simbit that includes 400.