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PSE open a puzzling class.
16 students join the class.
the classroom have 16 chairs arranged in (4 x 4) grid.

1   2   3   4
5   6   7   8
9   10  11  12
13  14  15  16

Students initials are A,A,D,E,E,G,I,M,N,N,O,R,S,U,U, and Y

These are the rules how they are placed in the class.

  • Both A are at chairs number 2,5,8 or 12 (take 2 chairs).
  • D is at chair number 1,5 or 10
  • Both E are at chairs number 3,7,10 or 12 (take 2 chairs).
  • G is at chair number 10 or 11.
  • I is at chair number 5,13 or 15.
  • M is at chair number 3 or 12.
  • Both N are at chairs number 1,4,5 or 16 (take 2 chairs).
  • O is at chair number 7,11,15 or 16.
  • R is at chair number 2,9 or 14.
  • S is at chair number 6,9 or 13.
  • Both U are at chairs number 1,4,6 or 14 (take 2 chairs).
  • Y is at chair number 3,8 or 11.
  • Both E must sit in the same row.

How are they arranged in the class?
There is a hidden message in the arrangement.What is the message ?

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Solved grid:

D A M N
A U O Y
R E G E
S U I N

And the message is:

DAMN YOU ARE GENIUS (if you read it as a snake)

How to solve it without writing a bruteforce algorithm:

Start with E, the clues are:

- Both E are at chairs number 3,7,10 or 12 (take 2 chairs).
- Both E must sit in the same row.

And the only possibility here is that E are in places 10 and 12. From here, start eliminating numbers and you will easily find all the other letters

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