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A yellow flyer with orange border. The top says "Barbeque on Sunday!" in large font. Right below is "You're invited to join us on our front lawn for a barbeque." In a white box near the bottom is "MENU:", then three lines of italicized food items, "Lamb chops & Steak", "Carrots & Peas", "Soda & Iced tea".

You were at your neighborhood barbeque when noticed a lady reporting a theft to the police. This is what you heard:

Lady: Help! A man grabbed my purse and ran away!
Police: Did you notice anything about him that can help us identify him?
Lady: Yes, he had a plate of peas.
Police: Only peas?
Lady: Yes.
Police: I see. Don't worry, we got this.

What happened? How did only the conversation above get the police confident in finding the thief?

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    $\begingroup$ Is this lateral thinking? Does the puzzle depend on information not in the puzzle not in the puzzle itself? $\endgroup$ – Chris Cudmore Feb 25 at 17:54
  • $\begingroup$ @ChrisCudmore No, it mainly depends on the conversation heard. The current below answers seem to have assumed some factors that aren't really true. $\endgroup$ – risky mysteries Feb 25 at 17:55
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    $\begingroup$ I think it's odd that there's such a prominent picture at the start of the question that turns out to have been a complete red herring. In my opinion, any prominent element of the puzzle should have a purpose, and a red herring that doesn't do anything else (even make a joke) doesn't have a purpose other than to annoy. It doesn't make the puzzle any more interesting. $\endgroup$ – bobble Feb 26 at 1:15
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    $\begingroup$ I'm sorry but I agree with @bobble on this one; you could remove the image and the entire puzzle would still make sense. $\endgroup$ – Tonks Feb 26 at 8:08
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    $\begingroup$ You accepted an answer that relies on the conversation, and said yourself that 'it mainly depends on the conversation heard'. The answer you linked would still be valid with or without the picture since there are no rules regarding how many people have peas, if the peas have to be served with other items etc included within the puzzle. You're adding a lot of rules in the comments to answers that aren't included in the puzzle, which suggests you have designed it to be a bit too broad despite you having an 'ideal' answer in mind. $\endgroup$ – Tonks Feb 26 at 14:25
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I think that

The woman actually said "A plate of Ps"

Meaning

The licence plate of the suspect is all Ps (probably custom made). This would help the police easily track him down.

Relevant XKCD

https://xkcd.com/1105/

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    $\begingroup$ Good answer, although the story rather implies that the thief escaped on foot - the man grabbed her purse and ran away. It's not out of the question, but it's a very strange and uninformative way to describe this method of escape. A slight rewording of the story "("the man grabbed my purse and escaped") would be equally ambiguous and not have this inconsistency. $\endgroup$ – Nuclear Hoagie Feb 25 at 18:25
  • $\begingroup$ @NuclearHoagie I noticed this. I intentionally used the word "ran" so to plant the picture of something other than a car. The definition of "ran away" does not whatsoever imply that it must be done on foot. $\endgroup$ – risky mysteries Feb 25 at 18:31
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Perhaps

the police merely followed the trail of peas that must have rolled off the thief's plate as he was running.

It should

lead right to him if he didn't run out of peas.

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  • $\begingroup$ No, as seen in the menu, there would be other guests with peas. $\endgroup$ – risky mysteries Feb 25 at 17:17
  • $\begingroup$ my obviously wrong thinking was that rot13(1) fvapr ur unq ab pneebgf ba uvf cyngr, gurl jbhyqa'g fgbc gur crnf sebz ebyyvat naq 2) bgure crbcyr jvgu crnf nera'g ehaavat naq ybfvat gurve crnf!) $\endgroup$ – SteveV Feb 25 at 17:20
  • $\begingroup$ I see. But nothing in the story indicated peas rolling off of his plate. $\endgroup$ – risky mysteries Feb 25 at 17:35
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Here's one possible solution,

The police looks for the person that only has carrots

And then,

Based on that, that person can tell them who they traded the peas for carrots with

Because,

If these are all pairs, then everyone would get either lamb chops and steak, carrots and peas, or soda and iced tea (because those are the different 'meals' on the menu.)

So,

The person with the carrots will tell who got their peas, & the police can track that person down.

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  • $\begingroup$ Though the carrots and peas were written on a single line, they weren't necessarily mixed up. Also, if they were mixed up, there's no reason why one wouldn't eat all their carrots first. $\endgroup$ – risky mysteries Feb 25 at 17:47

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