# PSE Advent Calendar 2021 (Day 22): Quick Math Card

This puzzle is part of the Puzzling StackExchange Advent Calendar 2021. The accepted answer to this question will be awarded a bounty worth 50 reputation.

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I found the strangest thing in my mailbox today. What could it mean?

Only the black symbols are relevant to the puzzle. Free background photo from pngtree.com

Text version:

$$☿-♀$$
$$⚷-(♂-\frac{◯}{\pi+\pi})=+(♂-\frac{◯}{\pi+\pi})$$

What a lovely thing to receive in the post :) It's a friendly message saying:

MERRY CHRISTMAS!

How do I know? We need to note that there are several different interpretations that can be ascribed to each symbol here...

Notably, these 'planet symbols' can be interpreted as relating to specific planets or specific metals. The ones we need to note here are:

☿ = MERCURY
♀ = COPPER (as well as the more immediately recognised 'VENUS')
♂ = MARS and IRON
⚷ = CHIRON

Additionally, we need to recognise that the large circle symbol (◯) here represents the circumference of a circle, whose formula is 2πr. This means that the repeated term '◯/(π+π)' can be seen as 2πr/2π - in other words: merely 'r'.

The message can then be parsed as follows...

☿ − ♀

MERCURY - CU (the Periodic Table symbol for copper) = MERRY

⚷ − (♂ − ◯/(π+π))

CHIRON - (IRON - R) = CHIRON - ION = CHR

=+

IS T

♂ − ◯/(π+π)

MARS - R = MAS

• @cap This is a lovely little rebus, cleverly using the same information in multiple ways. The quick solve is purely because I happened to be online when it was published and partly because I had a flash of inspiration that (surprising myself) turned out to be correct. A really nice little teaser, thanks :)
– Stiv
Dec 21, 2021 at 23:51
• Awesome. I got mercury minus Venus as the moon and then got even more confused!! Dec 22, 2021 at 3:12
• Thank you @Stiv and your answer is not only exactly right but also lived up to the question's title (Quick!) If you don't mind sharing, what was your flash of inspiration and thought process?
– cap
Dec 22, 2021 at 6:14
• @cap Sure rot13(V erpbtavfrq '2cv' va gur qrabzvangbe bs gur senpgvba naq fgenvtugnjnl pbaarpgrq gung gb pvephzsrerapr = 2cv*e, tvivat zr n jnl gb trarengr gur yrggre 'E'. Fcbggvat gung 'ZNEF - E' tnir zr ZNF ng gur raq, V svtherq V jnf ybbxvat sbe n jnl gb znxr PUEVFGZNF. Gur frpbaq hfr bs gur fnzr senpgvba unq zr pbashfrq sbe n fubeg juvyr (gjb ZNF'f nalbar?!) fb V ghearq gb gur svefg cneg naq abgvprq gung ZREPHEL jvgubhg PH jnf ZREEL. Guvf jnf jura V jbaqrerq vs gurfr flzobyf unq n frpbaq zrnavat V unqa'g cerivbhfyl xabja - naq Tbbtyr urycrq zr svaq gur zrgnyf, naq gur erfg pnzr gbtrgure!)
– Stiv
Dec 22, 2021 at 21:16