This was a logic puzzle that showed up on Gawker today, so I’ve modified it for posting purposes (I’ve posted the solution too, which you can see if you highlight the text below the problem)

Despite being enemies on the field, Bill Belichick and Mark Sanchez actually get along quite well.  While passing through Boca Raton on his way to scout some kids at the University of Miami and FSU, Bill stopped off for a drink with his erstwhile nemesis.

BELICHICK: [to bartender] Grumble grumble get me a Sam Adams, gotta keep those mouth-breathing idiots in Boston happy, you never know when there’s a camera around.

SANCHEZ: Captain and Coke, buddy.

[bartender steps away to fetch their drinks]

BELICHICK: [glances at doorway as a pair of women in cutoff shorts and halter tops enter the bar] Grumble grumble look at those chicks that just walked in.

SANCHEZ: [looks at the older of the two, frowns] that’s what happens when you get too much sun.  You’d think someone that spent so much time in a tanning bed would have sprung for the bolt-ons to go with the melanoma.

BELICHICK: Grumble grumble underinflated leather is what I like grumble grumble.

SANCHEZ: Looks like there’s grass on the field for the younger one, so I say play ball.  Should we run the single-wing offense?

BELICHICK: Coach calls the plays grumble grumble.

SANCHEZ: Sure thing, man, you take the lead.

[the men pick up their drinks and head over to where the women are standing at the bar]

BELICHICK: Grumble grumble are you two twin sisters?

LYNN: [giggles] Aren’t you charming!

ASHLEY: She’s my mom.  You won’t believe this, though, we actually have the same birthday.

SANCHEZ: No shit, when is it?

ASHLEY: [thinks for a moment] I’m not going to tell you, but I tell you what, if you can guess we’ll let you guys buy us a drink and we won’t even make sure the bartender lets us see him pour it.

SANCHEZ: Deal, but we’ll need a couple of hints.

[Ashley writes down a list of dates on a cocktail napkin:

May 15 — May 16 — May 19

June 17 — June 18

July 14 — July 16

August 14 — August 15 — August 17

]

ASHLEY: Now I’ll tell you the day…[whispers the day in Sanchez’s ear]…and Mom, you tell that silver fox over there the month.

LYNN: [whispers the month in Belichick’s ear].  Now when is our birthday?

BELICHICK: Grumble grumble I don’t know, but I know this dipshit doesn’t know either.

SANCHEZ: I didn’t know originally, but now I do!

BELICHICK: Now I know too grumble grumble bartender fix these ladies up.

What’s the women’s birthday?

The answer (highlight to see)

Belichick only knows the month.  But since he states that he’s certain Sanchez doesn’t know, he’s sharing the information that the birthday MUST be in a month (July or August) that doesn’t contain a unique number; otherwise Sanchez might know – it could be May 19 or June 18 and Sanchez wouldn’t need to know the month if it were either of those days (19 or 18).  

Once Sanchez has learned this – that it’s one of the days in July or August – he’s able to figure it out and says so, but also shares the information that he *couldn’t* have figured it out without knowing that it was in July or August.  Looking at the remaining dates (July 14 and 16, August 14, 15, and 17) Belichick can deduce that it couldn’t be the 14th (since then Sanchez wouldn’t now be able to know for sure).  Since Belichick knows the month, he tells us that he’s now figured out the day.

This tells *US* that it couldn’t be in August (since August contains two remaining days, the 15th and 17th, in which case Belichick wouldn’t be able to establish which day is the correct one) which only leaves July 16 remaining.  

So the answer is July 16.  And knowing what we do about Belichick and Sanchez, best guess puts the birth years as 1968 and 1994.

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