Hauts and Junior : Coalesce

COALESCE

As you travel from Iraq towards IIT Guwahati, after a long time you find yourselves on a mountain trail at Tehran, Iran. The mountain trail is diff cult and slippery. You suddenly get caught in a landslide and fall into a deep hole. Then the stones of 2 kg weight start falling onto you from above.

The hole is a 4x4 grid i.e., it is divided into 16 squares. Each square can accommodate only one stone (of any weight). To survive, you need at least one empty square. Owl notices your trouble and gives you the magical power to meld together stones, but only those of the same mass can be mould together. Since the stones are falling very fast, you are only able to push the stones in straight lines (horizontally/vertically).

For example, when the arrangement of one of the rows in fi gure 1 when pushed horizontally to left transforms as shown:

Question 15:

If one stone falls every second, what is the maximum time for which you can survive i.e., when no square is empty and all stones become immovable?

(A) (2^16) -1

(B) (2^17) -1

(C) (2^17) - 2

(D) 2^16

Question 16:

What is the largest stone that you can make if every second, either 2kg stone or 4 kg stones fall?

(A) 2^17

(B) 2^16

(C) (2^16) -1

(D) (2^17)-2