Equivalent Resistance

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If any among you have read I.E. Irodov , you would know that there is a problem based on an infinite mesh of resistances which has squares on it. To find the effective resistance between any two adjacent points we assign a current I in ward and I outward from the other point for a given V and get v/i ratio and hence get R equiv. But, incase we want to do it for diagonally opposite points , how should we proceed? This variantion came into my mind while solving it and couldnt figure how to go around it.
 

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