Puzzle:

The only way to get a free drink in this bar, is to prove to the barman that you are a friend of his boss. Here's how its done. You go to the barman, he tells you a number and you tell him the "countersign" number. If your answer is correct you get your drink. There's this mathematician who thought that there can't be a standard list of numbers and countersign numbers. There must be an algorithm that provides the answer from the number given by the barman. So he joins a party of three men who ARE friends of the boss and walks with them to the bar hopping to understand the algorithm from the three answers. HERE'S WHAT HE HEARD: The barman says "6" to the first man, he says "3" and got his drink. The barman said "12" to the second man, who replied "6" and got his drink. The barman said "14" to the third man and he answered "8" (!) and got his drink. Now its the mathematicians turn. "20", said the barman. What is the counter sign?

For Solution SCROLL DOWN...

Solution:

Six

You count the number of letters in the word. Twenty has 6 letters so the mathematician should say "six".

Six

You count the number of letters in the word. Twenty has 6 letters so the mathematician should say "six".

## 18 comments:

countersign is 1

here is the way....

for 6..3 ie,(6*3-3)/3=5 onelessthan 6

12..6 ie,(12*6-6)/6=11

again onelessthan 12

similarly,

for 20..(20*x-x)/x=19

so x=1

6 spelled as six ( 3 chars )

12 spelled as twelve ( 6 chars )

14 spelled as fourteen ( 8 chars )

20 spelled as twenty ( so 6 chars )

I think 6 is the answer

answer is 6

@srinu,

in (20 *x -x)/x = 19

that equation equal to 19x/x, so what ever value of x(except 0) , it equals to 19 .

So x can be any one of 1,2,3,..., -1, 1.2, -1.2, 2^(1/2) .......

So this is not the logic.

The Correct answer is 6

Logic: Guys there is nothing like mathematics in this puzzle.

Just write the number in words that the barman says. Count the number of letters in that word & that is the countersign number....

eg:

6 - SIX = 3 letters

12 - Twelve = 3 letters

14 - Forteen = 7 letlers

20 - Twenty = 6 letters

Yes the answer is 6 as described by Dhamendra

6. Countersign is number of letters in the "number" told by the barman. this puzzle would have been interesting if you didn't provide the vital clue 14!

(I wrongly typed as "number of words" instead of "number of letters" in my previous comment and was forced to delete it. Many apologies).

6 is the correct answer..

6

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It can be 14 also:

6 *2 = 12 +2 = 14 +6 = 20

3 *2 = 6 +2 = 8 +6 = 14

you say count the number of number 20 yeah its 6 but what is the connection of adding and multiplying its clear that six is just the only number that repeats twice so am i right or wrong????

Answer can be 17.

Reason: Mathematician used used quadratic interpolation to fit the three given answer i.e. in equation ax^2 + bx +c = ans. a=0.0625, b=-0.625 c=4.5

putting x=20 gives ans=17.

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