Intersecting lines inside a rectangle

Geometry Level 3

Assume that a 288 288 lines are passing randomly through a rectangle A B C D ABCD with B C = 12 and A B = 24 BC = 12 \ \text{and} \ AB = 24 . What is the minimum number of lines are required to intersect with all the 288 288 lines inside the rectangle?

HINT : the number of intersections will be ≥ 288 \ge 288 .


The answer is 2.

Ossama Ismail by Ossama Ismail , 63, Egypt

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1 solution

Ossama Ismail
Apr 21, 2018

Answer: Minimum number of lines = 2 lines, regardless of the number of lines passing through the rectangle

Just connect the TWO diagonals A C and B D AC \ \text{and} \ BD

The first diagonal A C AC intersects will all lines that connect A B to B C , A B to D C and A D to D C AB \ \text{to} \ BC \ , \ AB \ \text{to} \ DC \ \text{and} \ AD \ \text{to} \ DC

The second diagonal D B DB intersects will all lines that connect A B to A D and B C to D C AB \ \text{to} \ AD \ \text{and} \ BC \ \text{to} \ DC

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Nice Problem.

Hana Wehbi - 3 years ago

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