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There is a planet oz . The people there are four fingered and reside in 4 – dimensional space and thus the currency used by its residents are 3 – dimensional objects. The rupees notes are cubical in shape while their coins are spherical. However the coin minting machinery lays out some stipulations on the size of the coins.

· The diameter of the coins should be at least 16mm and not exceed 64mm
· Given a coin, the diameter of the next larger coin is at least 50% greater.
· The diameter of the coin must always be an integer.
You are asked to design a set of coins of different diameters with these requirements and your goal is to design as many coins as possible. How many coins can you design?

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TCS Other Question
Alice and Bob play the following coins-on-a-stack game. 50 coins are stacked one above the other. One of them is a special (gold) coin and the rest are ordinary coins. The goal is to bring the gold coin to the top by repeatedly moving the topmost coin to another position in the stack.Alice starts and the players take turns. A turn consists of moving the coin on the top to a position i below the top coin (0 ≤ i ≤ 20). We will call this an i-move (thus a 0-move implies doing nothing). The proviso is that an i-move cannot be repeated; for example once a player makes a 2-move, on subsequent turns neither player can make a 2-move. If the gold coin happens to be on top when it's a player's turn then the player wins the game. Initially, the gold coinis the third coin from the top. Then
a) In order to win, Alice’s first move should be a 0-move.
b) In order to win, Alice’s first move should be a 1-move.
c) Alice has no winning strategy.

d) In order to win, Alice’s first move can be a 0-move or a 1-move 21 people meet and shake hands. The maximum number of handshakes possible if there is no cycle of handshakes is
(A cycle of handshakes is a sequence of people a1, a2,....., ak such that the pairs (a1, a2), (a2, a3),.....(a(k-1), ak), (ak, a1) shake hands.
a) 17 b) 18 c) 19 d) 20