Puzzle 42 (HIGH) (Box + Comparison Based)

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Eight Boxes D, J, L, P, T, S, X and Y are arranged in ten shelves in which two of the Shelves are vacant. The Bottommost shelf is numbered 1 and the shelf above 1 is numbered as 2 and so on. Each Box has different weight.

It is also known that Box T is placed in a shelf which is a Square of the shelf number of fourth heaviest Box in a group. Box X is not heavier than Box S. Box D is not the lightest box and is placed in one of the shelves above Box T. At least one Box is placed above Box D. Box X is not placed below the seventh lightest Box. Number of Boxes placed above Box Y is as same as the number of boxes placed below Box S. Box L is heavier than Box S but lighter than Box Y. Heaviest Box is placed in a shelf number which is a multiple of 2 and one of the shelves above the heaviest box is vacant. Second heaviest Box is not placed at odd number shelves. Box T is not the heaviest box. Two Boxes are placed between Box J and Box P such that Box J is placed above Box P. Number of shelves between two vacant shelves is as same as number of boxes placed between Box D and Box Y. Sum of shelf number of two vacant shelves is one more than that of twice the shelf number of Box D. Box Y is not placed in odd numbered shelves. Box P is heavier than the box which is at shelf number 2. Lightest Box is placed at the shelf number 7.

Solution :

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