perplexus.info :: Logic : Paint Perception

Paint Perception (Posted on 2013-05-15)

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

There are 16 shelves on a wall which are arranged as shown in the diagram above. On each shelf there is a tin of paint, each containing a different type of Yellow. Using the following information, determine which type of yellow paint is on each of the 16 shelves.

Amber is below Fallow which is to left of Cream and Topaz.
Sulphur is below Buff and to the left of Primrose.
Cream is below Xanthic which is also to the left of Primrose.
Lemon and Guilded are to the right of Gold which is below Topaz.
Gamboge is to the left of Plain Yellow and above Aureate which is to the right of Sulphur.
Primrose is to the right of Aureate and below Gilt.
Saffron is above Lemon and below Gilt.

Note: To the left or right of refers to paint tins in the same row. Above or below refers to paint tins in the same column.

No Solution Yet Submitted by K Sengupta

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Logical Solution

Comment 3 of 3 |

Gilt is at the top of a column containing Primrose (6), Saffron (7), and Lemon (7).

Fallow is to the left of Cream and Topaz (1). Cream is farther left of Primrose (3) and Topaz is farther left than Lemon (4), so the Gilt column must be rightmost in the grid. {Gilt: 4}

Primrose and Xanthic are in the same row (3), which is not the highest row (6). Cream is therefore not in either of the top two rows (3), nor is Topaz in the bottom row (4), so the Fallow row must be the third one down. {Fallow: 9}

Xanthic and Primrose are in the second row (3,6). Saffron is above Lemon in the rightmost column (7). {Primrose: 8, Saffron: 12, Lemon: 16}

Amber must be in the lowest row (1). {Amber: 13}

Primrose and Xanthic are in the second row along with Aureate (6) and Sulphur (5). The leftmost element is not Primrose (6), Aureate (5), or Xanthic (1,3); it is Sulphur. {Sulphur: 5}

With Aureate in the second row, the top row contains Gamboge (5), which is to the left of Gilt and Plain Yellow (5). {Gamboge: 2, Plain Yellow: 3, Aureate: 6}

Thus Xanthic is finally the third element in the second row {Xanthic: 7}

Cream is below Xanthic (3) in the third column, so Topax is in the second column (1). {Topaz: 10, Cream, 11}

The top element of the leftmost row, above Sulphur, must be Buff (2). {Buff: 1}

The bottom row, with Amber on the left and Lemon on the right, also contains Gold (4) and to the right of that, Guilded (4). {Gold: 14, Guilded: 15}

The final arrangement, then, is:

1: Buff

2: Gamboge

3: Plain Yellow

4: Gilt

5: Sulphur

6: Aureate

7: Xanthic

8: Primrose

9: Fallow

10: Topaz

11: Cream

12: Saffron

13: Amber

14: Gold

15: Guilded

16: Lemon

Edited on May 17, 2013, 11:36 am

Posted by DJ on 2013-05-17 11:35:59

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