Self Maths Puzzle Numerical Ability Co-ordinate geometry

Imagine a square which has 4 corners and 4 edges. FOUR cats are there in all 4 edges, Rat enters the square in one corner and travels through edges , At each edge ,the hungry cat ate an X no. of rats , and remaining rats pass through next corner where each of rat gets doubled in number(if 2 rats enters ,4 rats leaves the corner) , then to next edge where the same X amount of rat is eaten and so on, twist is that Rat has to leave the square through same corner , but none left at the end!!! My queston is HOW MANY ENTERED THE SQUARE !, HOW MANY EQUAL NUMBER OF RATS ARE EATEN BY THE CATS ! (minimum possible value) remember that equal no. of rats are eaten by cats...... All the best

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Self Other Question

having 27 balls one ball is less weight.all are looking similar.with simple balance find minimum number of times we need to weigh to know which ball is less weight?? there are 4 persons to cross the bridge.only two persons can cross at a time and they are having only one torch.their speeds to cross the bridge is 1min,2min,5min,10min. if two persons cross the bridge they cross with slowest persons speed.what is the minimum and maximum time takes to cross the bridge??