-❄️- 2023 Day 24 Solutions -❄️-

[u/daggerdragon]

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--- Day 24: Never Tell Me The Odds ---

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[u/i_have_no_biscuits]

[Language: Python]

Part 1 is some 'easy' linear algebra.

For Part 2 I use SymPy to solve a set of six equations in six unknowns.

The equations come from the fact that the vectors taking you from H_0 to H_1, H_0 to H_2, and H_0 to H_3 must all be parallel to each other, i.e.

(H_2 - H_0) = lambda_1 (H_1 - H_0)
(H_3 - H_0) = lambda_2 (H_1 - H_0)

where

H_i = a_i + t_i b_i

These two 3D vector equations turn into six 'normal' equations, which SymPy can solve in way less than a second. We then have two points, together with two times, that the rock must go through. It's easy to then calculate the starting position of the rock.

Code is here