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Grandpa e mailed me a puzzle. Seemed very straightforward to me until I read it again.

"Are you sure this is right?" My e mail

"If there is a mistake- and I'm not saying there is- then it might lead you to the answer!"

This is what he sent me.

21 begins with a T

311 begins with a T

511 begins with an F

31 begins with an S

51 begins with ? Is it E or I or O ?

What do you think? What is the logic?

DrD
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    No 3D or Phone Codes. – DrD Jan 25 '21 at 23:08
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    Are these indices? The obvious answer is that if "511" begins with F so must "51" but that isn't an option. – humn Jan 25 '21 at 23:16
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    There is a fun clue in the puzzle. It was my "aha" moment! – DrD Jan 25 '21 at 23:23
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    That the statement separates "e" from "mailed" sticks in my craw. Everything else tickles me. – humn Jan 25 '21 at 23:27
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    I was thinking about digit sums, am I on the right track @DrD – Stevo Jan 26 '21 at 01:48
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    Because 21, 311, and 511 have odd ds, and then the letters that correspond is even numbered, and then 31, who has even ds, has a letter that is prime... – Stevo Jan 26 '21 at 01:50
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    Some observations: rot13(Gur yrggref ba gur evtug unaq fvqr ner gur fgnegvat yrggref bs gur svefg cevzr ahzoref: Gjb, Guerr, Svir, Frira - fheryl guvf pna'g or pbvapvqrapr? Rfcrpvnyyl jvgu R sbe Ryrira nf bar bs gur bcgvbaf sbe jung pbzrf arkg. Gur ceboyrz vf ubj gb rdhngr gurz jvgu gur YUF! Ybbxvat sbe xrljbeqf va gur grkg, 'yrnq' fgnaqf bhg - pbhyq gerngvat gur ahzoref nf N1M26 vavgvny cnvef ON, PX, RX, PN, RN creuncf pbeerfcbaq fbzrubj gb fbzr jbeyq YRNQREF? HF Cerfvqragf gur boivbhf bar. Ab qvpr fb sne sbe zr gubhtu!) – Stiv Jan 26 '21 at 12:06
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    Gurer vf n pbzzbanyvgl gb nyy gubfr YUF ahzoref gung znl tb onpx gb gur fgnaqneq xrlobneq. @Stiv – DrD Jan 26 '21 at 12:18

2 Answers2

16

I think the answer might be

O

Reasoning

Consider that, on a keyboard, the 1 is underneath the !
What if, instead of writing numbers like 3!, Grandpa forgets to use the shift button and writes 31 instead.
In this way, his numbers should read as follows

21 should be 2! = 2, which begins with T.
311 should be 3!! = 3, (using double factorial) which begins with T.
511 should be 5!! = 15, which begins with F.
31 should be 3! = 6, which begins with S.

and so

51 should be 5! = 120, which begins with O.

hexomino
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    Ah, this has to be it, surely! I was getting so consumed by the sequence I'd identified in comments above for the RHS that I couldn't see anything else - nice spot :) – Stiv Jan 26 '21 at 12:51
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    Xabjvat Tenaqcn, ur jbhyq sbetrg gur fuvsg ohggba vagragvbanyyl!! be vagragvbanyyl11 – DrD Jan 26 '21 at 13:29
  • That's some obscure math notation. In other contexts it would actually be read as a different operation. – Joshua Jan 26 '21 at 21:17
  • @DrD Ohg qvqa'g Tenaqcn hfr na rkpynzngvba znex va uvf ercyl gb lbh? – user Jan 26 '21 at 21:56
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    Nf V fcrphyngrq orsber Tenaqcn zhfg unir qbar gubfr guvatf gb vagragvbanyyl qvfgenpg naq gevpx zr. @user – DrD Jan 26 '21 at 23:06
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It seems too straightforward but here is my idea:

Twenty one : T
Three hundred eleven : T
Five Hundred eleven : F
Thirty one : T, but Grandpa made a mistake and took the letter just before T: S
Fifty one : F, but if we make the same mistake we get E

Pepper
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    Or "S" for "Sorry, I can't remember how to spell 31" which leads us to "Oh well, same for 51, damn Alzheimer's disease"... Yes a bit too straightforward but may interest others anyway. Welcome to puzzling.SE! – xhienne Jan 26 '21 at 10:14
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    To whoever upvoted: Thank you but you didn't have to, I knew it was too literal and most likely wrong when I posted this answer (maybe I should have specified "initial idea"), so I don't mind it being downvoted :) It will take more than a few downvotes to scare me away! – Pepper Jan 26 '21 at 11:15
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    That was a welcome vote, it only happens once in a lifetime :-) Your reasoning is not that bad; I guess it is the same reasoning that led the poster ask "Are you sure this is right?" Now try to figure out Grandpa's answer... – xhienne Jan 26 '21 at 11:22
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    Welcome to PSE, Pepper :) Some inside information: DrD's "Grandpa" puzzles (long-established here) usually involve some clever trick of lateral thinking. There will turn out to be something where this sequence of statements makes perfect sense, and he has deliberately chosen cases which appear to satisfy a different rule on the surface (namely initial letters of numbers)... until a certain point when your mind goes "What?!" Your answer here if correct would definitely be far too straightforward for one of these puzzles (as you suspected). But keep thinking! – Stiv Jan 26 '21 at 12:02
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    @Stiv Thank you for the context, I'll be eagerly waiting for Grandpa's next puzzle! (and taking a look at the previous ones too) – Pepper Jan 26 '21 at 13:49
  • Hello @Pepper. Welcome to PSE. Try this one first. It is kind of wacky. Enjoy.https://puzzling.stackexchange.com/questions/68939/grandpas-crazy-math-another-grandpa-mystery – DrD Jan 26 '21 at 19:56