perplexus.info :: Just Math : Optimizing triangulation moves

Optimizing triangulation moves (Posted on 2025-02-26)

Alice has three pins, labeled A, B and C, respectively, located at the origin of the coordinate plane. In a move, Alice may move a pin to an adjacent lattice point at distance 1 away. What is the least number of moves that Alice can make in order for triangle ABC to have area 2024?

No Solution Yet Submitted by Danish Ahmed Khan

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Solution

| Comment 1 of 2

The area of any lattice triangle is half the area of the horizontal/vertical rectangle that bounds it. If A is moved horizontally and B vertically, you may as well leave C at the origin. For simplicity move right and up and call A=(a,0) and B=(0,b).

We then seek minimum a+b such that ab=4048.

4048=2^4*11*23, sqrt(4048)=63.6

The closest we can get is 46*88=4048 and so the number of moves is 46+88=134

Posted by Jer on 2025-02-26 14:35:45

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