35:T522,A supermarket has to place 12 items (coded A to L) in shelves numbered 1 to 16. Five of these items are types of biscuits, three are types of candies and the rest are types of savouries. Only one item can be kept in a shelf. Items are to be placed such that all items of same type are clustered together with no empty shelf between items of the same type and at least one empty shelf between two different types of items. At most two empty shelves can have consecutive numbers. $$\newline$$ The following additional facts are known. $$\newline$$

A and B are to be placed in consecutively numbered shelves in increasing order.
I and J are to be placed in consecutively numbered shelves both higher numbered than the shelves in which A and B are kept.
D, E and F are savouries and are to be placed in consecutively numbered shelves in increasing order after all the biscuits and candies.
K is to be placed in shelf number 16.
L and J are items of the same type, while H is an item of a different type.
C is a candy and is to be placed in a shelf preceded by two empty shelves.
L is to be placed in a shelf preceded by exactly one empty shelf.

36:T443,—-- | Shelf No | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | |------------|---|---|---|---|---|---|---|---|---|----|----|----|----|----|----|----| | Item Code | - | - | C |H/G | G/H | - |L | A | B | I/J |J/I | - | D | E |F | K | | Item type | - | - | C | C | C | - | B | B | B | B | B | - | S | S | S | S | | Shelf No | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | |------------|---|---|---|---|---|---|---|---|---|----|----|----|----|----|----|----| | Item Code | - | L | A | B | I/J | J/I | - | - | C | H/G | G/H | - | D | E |F | K | | Item type | - | B | B | B | B | B | - |- | C | C | C | - | S | S | S | S | |Item Type | Item code | |---------|---------| | Biscuits (5) |I, L, J, A, B | | Candies (3) | C, H, G | | savouries (4) | D, E, F, K | The number of arrangements for the first case = 2*2=4 The number of arrangements for the second case = 2*2=4 The total number of arrangements = 4+4=8.37:T1d21,

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