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Answering boolean question without knowing "Who" answer

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Can cryptography solve this problem?

Two people are chatting, Mr. X and Ms Y. They give each other a CRC16 hash of someone's name initials and salt a random number at the end (suffix).

Ms Y: "I love someone with the initials {53d4}".

Mr X: "Are that person's initials {da17}?"

{CRC16} -> Original String
{53d4} -> A7777
{da17} -> X123

This means, Ms. Y loves someone with initials name A and Mr. X thought it was someone with initials name X.

How can they both know answer of Mr.X's question WITHOUT knowing the guessed person's initials? So the expectation is to know only the boolean answer, YES or NO without knowing who the person is, no matter who is it. I mean, X shouldn't know who is it and Y shouldn't know who the person of X thought.

Note: You can modify dialogue or totally change dialogue as long as it answers the how question.

I sit in a Tesla and translated this thread with Ai:

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Most people don’t grasp that asking a lot of questions unlocks learning and improves interpersonal bonding. In Alison’s studies, for example, though people could accurately recall how many questions had been asked in their conversations, they didn’t intuit the link between questions and liking. Across four studies, in which participants were engaged in conversations themselves or read transcripts of others’ conversations, people tended not to realize that question asking would influence—or had influenced—the level of amity between the conversationalists.