A party is being held at a local mansion. The host is very rich and his success is because of one thing ~ his famous recipe for Spaghetti!

The only guests that may attend are people the host knows and trusts, whom he gave the password to enter to. But, Since over 20 of his secret recipes are stolen, he has decided to change the method a bit.

Here's where you come in. You and a friends are trying to steal this recipe. You and 2 of your friends sneak behind the trees.

But instead of saying the number and asking the password, the guards/security stopped all the guests at the entrance. After ten minutes the Security Head made an announcement: "All the guests are requested to gather here in front of the gate. No body will be allowed to enter if arrive after the procedure".

You and your friends got tensed and the only option in front of you to steal the recipe is taking the chance and go there and stand among the guests hoping you will be able to figure out the password. But one of your friends ran home leaving you and your friend fearing about getting tampered by the elephant and all.

You and your friend went there and stood with the guests. There was a total of 16 guests including you and your friend. The guards made all the guests ( along with you and your friend ) to stand in a 4x4 (4 rows and 4 columns) arrangement and provided a paper and pen. You were standing in the 3rd row from front and 3rd column from left. Your friend was standing on your right ( that is 3rd row from front and 2nd column from left )

Then the Head Guard shouted "144"

You don't know what to write and what to do. You started to sweat. You tried to peak to the answers written by some of the guests standing near you. You were able to see the answers written by a guest standing your left, front left (diagonal position), front, front-right (diagonal position), and your friend standing on your right.

  • The guest on your left wrote : 12
  • The guest on your front-left wrote : 18
  • The guest on your front wrote : 24
  • The guest on your front-right wrote : 36
  • Your friend (on your right) wrote : 52

Now, What number you will write in order to get into the party and steal the recipe.

Additional Question: Did your friend wrote the correct password, or did he get tampered by the elephants?

Note: Please place your answers in spoiler tags. Also mention how you get to the answer.

Feel free to edit the question to fix grammatical errors. ;)

Hint (Check it only if you can't find the answer without any hints):

The position of guests whose answers you saw during the procedure are mentioned relative to your position. Try finding there actual position first and then try solving)

New Edit

enter image description here

The one with the big mustache is the Head Guard. You are the one in red color and your friend is the one in blue, that is at your right, considering you are facing towards the guard. The rows and columns are mentioned in the question from the Head Guards's perspective (To make the solution a little more difficult). That is row 1 is the first row in front of him. Column 1 is the left most column in front of him.

  • $\begingroup$ Promising. Trying to solve. Do not look excessively hard nor excessively easy. $\endgroup$ – Victor Stafusa Nov 13 '14 at 7:48
  • 2
    $\begingroup$ Your directions relative appear to be incorrect. Your friend can't be on your right in the 2nd column from the left if you yourself are in the 3rd column from the left. He would have to be on your left in that case. $\endgroup$ – JamesENL Nov 13 '14 at 7:54
  • $\begingroup$ I second @JamesMassey Is your friend in the 2nd or in the 4th column? $\endgroup$ – Victor Stafusa Nov 13 '14 at 8:07
  • $\begingroup$ I considered numbering the rows and columns starting from front left. I will try creating a graphical representation and will update the question with it so that it will be easier for understanding the layout. $\endgroup$ – AeJey Nov 13 '14 at 8:24
  • 2
    $\begingroup$ I second @AE :-) $\endgroup$ – Rand al'Thor Nov 15 '14 at 19:36

My guess is this:

This is the layout of the numbers:

??? ??? ??? ???
18 24 36 ???
12 YOU 52 ???
??? ??? ??? ???

12, 18, 24 and 36 all divides 144. 144 is a number with many divisors (144=2*2*2*2*3*3).
Well, 12=18*2/3, 24=18*4/3, So, you=24*2/3=12*4/3=16
And the friend is doomed, 52=2*2*13, and 13 is not a divisor of 144.
Since 36=24*3/2, his number should be 36*2/3=16*3/2=24

EDITED: New layout.


So you are

From guard's perspective multiply row & column, and divide 144 by that

And friend

poor friend should have done 12


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