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GATE CSE 2022 Q10: Least extra ropes to split a plot into four similar plots

Question

A plot of land must be divided between four families. They want their individual plots to be similar in shape, not necessarily equal in area. The land has equally spaced poles, marked as dots in the below figure. Two ropes, R1 and R2, are already present and cannot be moved.

What is the least number of additional straight ropes needed to create the desired plots? A single rope can pass through three poles that are aligned in a straight line.

A square grid of equally spaced poles enclosed by a boundary with two cut corners (top right and bottom left); rope R1 runs horizontally from the left edge and rope R2 runs vertically down from the top edge
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Try it: multiple choice: exactly one correct option

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Answer: D (official GATE 2022 final answer key)

Concept used: Spatial reasoning: the four plots must have the same shape, so each needs the same cut-corner outline as the whole land.

First step: Note the land is symmetric about the diagonal through the two cut corners; try extending R1 and R2 and adding ropes so each plot is a scaled copy of the outline.

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Source: official GATE 2022 CS question paper and final answer key, organised by IIT Kharagpur. Question paper · Answer key

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