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My parents are the same whether I travel from Attu Island to Caroline Island or from Caroline Island to Attu Island.

The mother sandwiches an 8 between the highest numbers. If she replaces 8 with 92, she still remains my mother but becomes quiet.

The father sandwiches a 1 between the halves of the highest numbers. If he replaces 1 with the smallest number, he has performed.

Who are my parents?

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MOM and DAD

Clue 1 indicates that

they're both palindromes.

Clue 2:

8 on the periodic table is O, and M is the largest single-letter Roman numeral (without getting into bars above the letters). 92 on the periodic table is U, giving MUM.

Clue 3:

1 stands in for A, following the old A=1 B=2 ... Z=26 method. If you replace the A with an actual 1, it looks like I, giving DID.

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    $\begingroup$ Rot13: Jung vf gur fznyyrfg ahzore va Ebzna ahzrenyf? ; ) $\endgroup$
    – ACB
    Commented Aug 26, 2022 at 4:38
  • $\begingroup$ Note that rot13(Nggh Vfynaq naq Pnebyvar Vfynaq ner gur jrfgrea naq rnfgreazbfg vfynaqf va gur jbeyq erfcrpgviryl. (Nygubhtu grpuavpnyyl, Nggh vf va gur rnfgrea urzvfcurer, gurl zbirq gur Vagreangvbany Qngr Yvar gb vapyhqr vg jvgu gur erfg bs Nynfxn.) Nalubj, gur rnfg-jrfg/jrfg-rnfg guvat vf zrnag gb pyhr vagb cnyvaqebzrf.) $\endgroup$
    – Darrel Hoffman
    Commented Aug 26, 2022 at 17:36

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