Correct spelling, explanation: this is the correct form of thirty-first because the end of this ordinal number is -st and so should be the ending of the numeral form. This is basically the rule for all ordinal numbers: third is 3rd, thirty-first is 31st, and fifty-fourth is 54th. Therefore 31th is incorrect.

Definition of 31st:
numeral, the ordinal number between 30th and 32nd
On Jack’s 31st birthday we had a huge party.
It’s crazy, it’s your 31st job!

Incorrect spelling, explanation: 31th is incorrect because the word thirty-first doesn’t end with th but with st. 31st is thus the correct form. Ending -st is added to the number first and any other ordinal number ending with first, so 31st is the correct form.

Incorrect spelling

Incorrect spelling