Medium puzzles




Medium Discrete Maths

A rectangular table has 100 coins with unit radius, placed on it such that none of the coins overlap, and it is impossible to place any more coins on the table without causing an overlap. Using this specific configuration, find a special configuration of 400 coins which covers the table with overlaps.

Covering means for every point on table there is a coin above it.

Hint
Solution
Source: CSEblog
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Medium Discrete Maths

On a table you have a square made of 4 coins at the corner at distance 1. So, the square is of size 1×1. In a valid move, you can choose any two coin let’s call them mirror and jumper. Now, you move the jumper in a new position which is its mirror image with respect to mirror. That is, imagine that mirror is a centre of a circle and the jumper is on the periphery. You move the jumper to a diagonally opposite point on that circle. With any number of valid moves, can you form a square of size 2×2? If yes, how? If no, why not?

Hint
Answer
Solution
Source: Saurabh Joshi's Blog
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Medium General

What is/are the next term(s) in the sequence:
a) 1, 11, 21, 1211, 111221, ?
b) 10, 11, 12, 13, 14, 20, 22, 101, ?, ?
c) (This a sequence made by only 2 & 1): 2,2,1,1,2,1,2,2,1, ?, ?....

Hint
Solution
Source: Common
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