# WAS IT A CAT I SAW? Do Some Detective Work & Catch The Imposters

Carolina County Community Cat Conference is going on at a resort exclusively reserved for Prime Members.

Some look-alike impostors, aka cats, have sneaked in. They all wear fancy name tags that reveal their character.

Toss on a Sherlock Holmes hat and catch these cunning cats, that is the imposters, by examining their name tags closely. Initially assume all are Prime Members, unless you notice a specific character in the name tag that reveals that it they are not a Prime Member, and instead are actually a cat.

Only basic knowledge of primality test is needed to catch the culprit.

1) was it a rat I saw

2) Tacocat

3) Madam I m Adam

4) Malayalam

5) Dammit I m mad

6) Step on no Pets

7) Never odd or even

8) Do geese see god

9) Toppot

10) Redder

11) Race fast safe car

12) Madam in Eden I m Adam

• Is the mathematics tag meant to be there? – gabbo1092 May 22 at 14:20
• Yes..need to understand prime properties – Uvc May 22 at 14:21

## 3 Answers

Partial answer

(I don't intend to make this less partial because that feels like a computer-based slog.)

I assume the idea is that each of these represents a prime number whose digits form the palindromic pattern given by the letters. Well,

any with an even number of digits must be an impostor, because any palindrome with an even number of digits is a multiple of 11. That means 6,7,9,10 are impostors.

My guess is

that the odd-length ones (including the Dammit... one if "I am" becomes "I'm") all do have corresponding primes. But actually checking that seems really tiresome. Also, it's kinda ambiguous whether we're supposed to assume that different letters correspond to different digits.

• Garetth...Great quick detective work – Uvc May 22 at 14:28
• Isn't this.. a bit far-fetched, given the current description? o.O – athin May 22 at 14:29
• It is surprising how the puzzles are dissected..if all the information is given explicitly, then no fun..club is primarily for prime numbers..stated..as a detective you have to examine the character and identify the distinguishing features from the majority. You identify the suspects and you can state your assumptions in doing so. – Uvc May 22 at 14:38
• No, what I mean is that given the statement of the problem, I'm kinda think it's (a bit) too board. No clue or statement to hint or give the impression that each character represent a number. The Prime Member is not enough. I also answer all composite numbers to be the impostors. I can also count the letters, or summing the A1Z26 and pick the non-prime one. My answer is also possible despite not taking the prime as a step. Additionally, as Gareth also stated, there are still many ambiguous steps like different letters should be different numbers so similar idea may lead to different answers. – athin May 22 at 15:35
• I originally toyed with that idea..then it will be too easy.. I will take suggestions and add edits to make it easy for future readers ..in real life, detectives life is not easy.. – Uvc May 22 at 15:49

It's

Number $$5$$ as it's the only one which is not palindrome.

• Ah, beat me to it! – PartyHatPanda May 22 at 14:19
• I suspect #5 is meant to say "I'm" rather than "I am". – Gareth McCaughan May 22 at 14:21
• @athin..all palindromes need not be primes..see Garett’s explanation – Uvc May 22 at 14:41

The immediate one that stands out is

Number 5, as it isn't a palindrome

• Need to more detailed detective work – Uvc May 22 at 14:21