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Since I was a kid, nobody wanted me in their super-exclusive clubs... the "House in the Tree Club"... the "Girls Only Club"... the "Whatever you are NOT Club"... but now that I am a skilled (and a bit nerdy) guy, time has come to take my revenge!

I've just discovered that not far from my house in New York City, there's a secret place where some guys seem to meet every week. I don't know what kind of club it is, but I definitely want to be a part of it!

Every night, each member knocks at the door of the Secret Club, and each time, a voice comes from inside, asking some strange questions...

At this very moment, someone is knocking on the door... ( - Let's listen to what they say... - )

"Knock! Knock!"
"Who's knocking?" asks the voice.
"I am a member Sir, let me in!" answers the guy.
"If you're a member, tell me what are the results of these operations: 17 + 5? 24 + 3? 1 + 16?".
"Of course... 22... 27... 17!" is the guy's response.
"Very well! Come on in!".

(- Well, I guess it's not the MENSA Club... - I think...)

A second guy approaches the door, knocks at it, and again the same scene takes place:

"Prove that you're a member! Answer these: 38 - 37? 28 - 10? 14 + 4?"
"Ehm... 1... 18... and again 18!".
"Good boy! Come in and take a seat near the other guys!".

(- OK, it must be some sort of math-nerd association... but better than nothing!...)

One last guy knocks at the door, but this time the question they ask him is very very strange...

"Well, if you are really one of us, tell me... What's our special number... the one with the unique property we all know?..."
The third guy seems slightly surprised... keeps thinking for a while, and then shouts: "Ah ah!.. You're referring to 12! Are you?".
The voice from inside the house starts laughing "Ah ah! For sure you are one of us!", opens the door and lets the guy in...

(- Well... I am a bit disappointed... but I'll give it a try... I'm sure they'll let me in!-)

"Knock knock!... ehm... I'm a member! Let me in!"
"Are you sure? If so, tell me... What's the result of 11 + 1? 10 + 17? 21 + 3?"
"...Ehm... 12... 27..." I start answering...
"OK... and what about the last one?" says the voice
"24!!" I shout... just a second before the guy from inside starts to yell:
"You liar! Go away and never come back to this respectful club!!"

At the end of this shocking experience, I still have a question in my mind:

"WHAT KIND OF CLUB WAS IT THAT I WAS TRYING TO ENTER?"

HINT 1:

The club is a real club. Many clubs like this one exist in real life. Probably, many members of the Puzzling Community are members of such a club in real life. Of course, the secrecy about the club is purely "fictional" and for the purpose of the puzzle.

HINT 2:

One of my guesses about the club's members was completely wrong: they ARE NOT "math nerds", and you don't need particular math skills to solve the calculations asked by the man at the door. Anyway, not everybody could answer those questions like the members did.

HINT 3:

Pay attention to the tags: no is present...

HINT 4:

It appears that the right answer to the last question of the man at the door should have been "23" instead of "24"...

HINT 5:

In my last edit I added a location for the story. Though it is not strictly necessary, it could be important to solve the puzzle.

HINT 6:

Twelve is "special" for club's members, because is the only number with a specific characteristic; anyway it's not so obvious, that's why the member who was asked about it had to think a while before answering...

Hunter
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    Could it be 'the kind of club you aren't in'... Or possibly another "Whatever you are NOT Club". ;}? – Mark N Jun 17 '15 at 17:00
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    More likely, the door guy knows all the members, and the password thing is just a fun addition. He just doesn't know you :P – Set Big O Jun 17 '15 at 17:03
  • The Club is a real one. And, of course, all the questions are relevant to the solution... ;-) – Hunter Jun 17 '15 at 17:06
  • if 12 is a special number it might be that 12 and 21 are changeable so 12 = 21 and 21 = 12 so 21 + 3 = 15 –  Jun 17 '15 at 17:16
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    @SvenB It could also just be "all answers which are multiples of 12 will be given as 12", but I'm hoping for something a bit more obvious (once seen). – Set Big O Jun 17 '15 at 17:19
  • @SvenB Nope. 12 has a really unique property (at least for members of that specific club) – Hunter Jun 17 '15 at 17:22
  • What kind of club was it? Easy! A strange club! – leoll2 Jun 17 '15 at 17:26
  • Can you confirm that 17 + 5 = 22? – Engineer Toast Jun 17 '15 at 18:37
  • @MarkN Using base 12 wouldn't be a special property of 12, though, as OP has mentioned is required. I do want to rule out the possibility, though. – Engineer Toast Jun 17 '15 at 18:37
  • I think I'll add some hints to the puzzle, to put you on the right track. For now I can just tell you that one of my guesses about the club was totally wrong (just like all the answers you gave till now! ;-)) ... – Hunter Jun 17 '15 at 20:47
  • Possibly, I'll add a second part to the puzzle, a sort of "day two" of the story... Ah, and maybe knowing the right answer to the last question of the guy at the door could help you. Maybe. ;-) – Hunter Jun 17 '15 at 20:50
  • 27 may be answer to that question. – Rafee Jun 17 '15 at 21:38
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    Would the results differ if the doorkeeper always said "you are" instead of "you're" ? – Hagen von Eitzen Jun 17 '15 at 21:53
  • @HagenvonEitzen No, same answers. There aren't tricks of this kind in the puzzle. – Hunter Jun 18 '15 at 05:31
  • @EngineerToast: Yes. 17+5=22. Probably not for the reason you are suspecting. – Hunter Jun 18 '15 at 06:59
  • I think maybe he should have answered something like "the special number" for the last one instead of 12...other than that, I have no idea. Maybe the Special Number Club? – BethM Jun 17 '15 at 19:59
  • Twelve is special for club's members, because is the only number with a specific characteristic; anyway it's not so obvious, that's why the member who was asked about it had to think a while before answering... – Hunter Jun 18 '15 at 07:03
  • wild guess :) is it related to zodiac? – Hershey Jun 18 '15 at 08:52
  • @Hershey Nope. Horoscope is something I hate even more than hard mathematics! ;-) – Hunter Jun 18 '15 at 08:55
  • Is it something related to footballs? – FunkTheMonk Jun 18 '15 at 09:43
  • @FunkTheMonk: No. And the information you require to solve the question asked by the man at the door are not too specific or too difficult if you are a member. So what has been asked is not related to some famous episode of the past, or any other event in the past important or memorable for that community. – Hunter Jun 18 '15 at 09:49
  • Is it something related to something nonsensical such as 9 + 10 = 21? – user41805 Jun 18 '15 at 09:58
  • @KritixiLithos: No. All answers are extremely straight and logical. – Hunter Jun 18 '15 at 10:02
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    Are there any more tags which can be added to the questions? – user41805 Jun 18 '15 at 10:03
  • @KritixiLithos: your question is extremely pertinent. Selecting the right tag was one of the biggest problem I had writing this puzzle. I chose the enigmatic-puzzle one because I didn't want to give away too much information. But for sure there are some other tags that could be added. – Hunter Jun 18 '15 at 10:08
  • Sounds like the club is related to a tag? – FunkTheMonk Jun 18 '15 at 10:54
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    @KritixiLithos : Pay special attention to hints n. 2, 5 and 6. In particular n° 5: why could location be important to solve the puzzle? It would not, if it was just a "math question"... It's clear that calculations in the puzzle are not just a matter of maths (even if they are in some way straight calculations...) – Hunter Jun 18 '15 at 12:12
  • Ah... and make sure you have completely understood hint 6 (pay attention even to single words / formatting... ;) ) – Hunter Jun 18 '15 at 12:20
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    @Hunter "The word "twelve" is the largest number with a single-morpheme name in English." Are you referring to this? – dmg Jun 18 '15 at 12:29
  • @dmg Nope. But good try. And very interesting point of view... ;) – Hunter Jun 18 '15 at 12:32
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    @Hunter I was trying to utilize your statement "because is the only number with a specific characteristic", so other words, which are not numbers, may share that characteristic. – dmg Jun 18 '15 at 12:45
  • @dmg My comment wasn't ironic: your point of view is one of the most interesting I've read so far, probably the closest to the solution (yet, still far from it). Your posts could be really useful to get on the right track (maybe you already are... ;) ) – Hunter Jun 18 '15 at 12:57
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    @Hunter I wasn't implying it was ironic. And it seems that it was about the words after all :) – dmg Jun 18 '15 at 13:01
  • @Hunter Thank you for the information. – user41805 Jun 18 '15 at 16:02
  • You need to revise Hint #6. "One hundred five thirds" and "negative two hundred eight fourths" both meet that criteria. Granted, they can be reduced to 35 and -52 but they're still valid numbers. (Yes, I spent too much time on this but it's a really neat factoid!) – Engineer Toast Jun 18 '15 at 16:11
  • Only thing I can think of is a baking club. When a baker bakes a dozen donuts, he or she usually makes 13, which is known as a "Baker's dozen." – Kingrames Jun 18 '15 at 12:41

4 Answers4

56

The club is a

Scrabble club

The calculations are

the scrabble values of the letters. For example TWENTYONE = 15 THREE = 8

So the answer for 21+3 is 23.

Twelve is a special number, in that

it has its own scrabble score: T (1) W (4) E (1) L (1) V (4) E (1) gives a total of 12

Edit from the OP:

This is the point values of each tile in the American-English version of Scrabble (that's why I added the reference to NYC as a location for the story) : A=1, B=3, C=3,D=2, E=1, F=4, G=2, H=4, I=1, J=8, K=5, L=1, M=3, N=1, O=1, P=3, Q=10, R=1, S=1, T=1, U=1, V=4, W=4, X=8, Y=4, Z=10

According to it

these are the values of each number/word mentioned in the puzzle: ONE=3, THREE=8, FOUR=7, TEN=3, ELEVEN=9, FOURTEEN=11, SIXTEEN=14, SEVENTEEN=12, TWENTYONE=15, TWENTYFOUR=19, TWENTYEIGHT=21, THIRTYSEVEN=20, THIRTYEIGHT=21

Hunter
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Fillet
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  • What is the connection between NYC and the answer? – FunkTheMonk Jun 18 '15 at 12:50
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    @FunkTheMonk The number and scores of the tiles are based on frequency analysis of the New York Herald Tribune and the New York Times, the English Dictionary and the Saturday Evening Post. – dmg Jun 18 '15 at 12:52
  • @FunkTheMonk Maybe NYC is on a grid, like scrabble? – Fillet Jun 18 '15 at 12:56
  • I just got this, clicked into the tab to reply, and then your answer loaded. Grr... Although I didn't get twelve's special property, so congratulations, too – LowIntHighCha Jun 18 '15 at 13:00
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    NYC was also the site of the first National Scrabble Championship in 1978. Maybe the club was formed around then? – Set Big O Jun 18 '15 at 13:03
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    Value of letters are different in other languages. I added NYC to point that the puzzle is based on the american/english letters scoring. – Hunter Jun 18 '15 at 13:13
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    @LogicianWithAHat: At times like this, it is good to think about how solving puzzles keeps your brain fit and happy for the future, and at least you know in your own mind you solved it. Much more important than internet points (cut to shot of me throwing internet points into the air, then diving into internet points) – Fillet Jun 18 '15 at 13:56
  • @Hunter Is this the right answer? – user41805 Jun 18 '15 at 16:10
7

I think the answers should've been

12, 27 and 16

The third guy revealed something about the number 12. It could possibly be some sort of key pre-decided by the club.

The first guy answered 22, 27 and 17.

27 - 22 = 5, or 05
5 - 0 = 5
12 + 5 = 17 i.e. the third number

The second guy answered 1, 18 and 18.

18 - 1 = 17
7 - 1 = 6
12 + 6 = 18 i.e. the third number

The pattern I guessed is

Do simple arithmetic calculation on the first two operations.
Subtract the first number from the second number, if the result is a two digit number, do the subtraction again.
Add the final result to 12.

So accordingly,

12 and 27 are obtained from the first two operations
27 - 12 = 15
5 - 1 = 4
12 + 4 = 16

What kind of club it was, I couldn't figure it out.

Jeet Parekh
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Since the tag is lateral thinking, My thought is

It's Dozen club. A club of 12 people.

All the other members were admitted because they answered the numbers correctly. And the question "What's our special number" was asked to the 12th person. Their special number is 12 since they have 12 members. Since all the 12 members were present you were not admitted. The guard already knew you are not a member and that's why he said "Are you sure? If so, tell me.." at the beginning. Then he asked the question to play with you. Whatever answer you give, he will kick you out. If you have knocked the door before the 12th person, you would have been admitted.

AeJey
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  • Good supposition, but this isn't the answer to the puzzle. I've added the lateral-thinking even if this is not a classic lateral-thinking puzzle (even if it contains a part of "laterality"). For sure it is NOT a calculation puzzle (and this is what I wanted to clarify...) – Hunter Jun 18 '15 at 08:34
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I'm not sure, but i'm guessing it has to be something about the pattern of the answers..?

Since all the answers repeat digits i guess the pattern is like this:

The first one three 2s and two 7s, the second one three 1s and two 8s... so i guess the answer should be a number with those patterns... so, my answer to the last sum is either 12 or 21, as there're already two 2s, a 1 and a 7 (you could say it could also be 72 or 27, but their special number is 12).

Anyway, great puzzle.

McFly
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  • No, I'm afraid you'r on the wrong track. Anyway a solution like the one you propose does not answer the question, i.e. what kind of club we are dealing with. When you understand how to interpret the calculation in the puzzle, the answer to the very last is pretty rethorical/obvious... – Hunter Jun 18 '15 at 08:38