From 95261557ea4f03af0403f384a56df4235c978996 Mon Sep 17 00:00:00 2001 From: Dory Date: Mon, 25 Dec 2023 13:20:40 -0800 Subject: [PATCH] d24p2 --- 24/test.txt | 22 ++++++++++++++++++++++ 1 file changed, 22 insertions(+) diff --git a/24/test.txt b/24/test.txt index 35963dc..cffefba 100644 --- a/24/test.txt +++ b/24/test.txt @@ -3,3 +3,25 @@ 20, 25, 34 @ -2, -2, -4 12, 31, 28 @ -1, -2, -1 20, 19, 15 @ 1, -5, -3 + +Using first 3 rays + +x + a*t1 = 19 - 2t1, y + b*t1 = 13 + t1, z + c*t1 = 30 - 2t1, +x + a*t2 = 18 - t2, y + b*t2 = 19 - t2, z + c*t2 = 22 - 2t2, +x + a*t3 = 20 - 2t3, y + b*t3 = 25 - 2t3, z + c*t3 = 34 - 4t3 +9 eqs, 9 unks, thus solution in 3 points. +--> a = -3, b = 1, c = 2, t1 = 5, t2 = 3, t3 = 4, x = 24, y = 13, z = 10 + +x+a*t1 == 320870677764563-40*t1, y+b*t1 == 335750934489987-24*t1, z+c*t1 == 282502845957937+10*t1, +x+a*t2 == 219235623600942+127*t2, y+b*t2 == 408022798608755-45*t2, z+c*t2 == 245679379684914+66*t2, +x+a*t3 == 171834827764229-122*t3, y+b*t3 == 225154401936948-521*t3, z+c*t3 == 232302441670972+95*t3 + +sage: x, y, z, a, b, c, t1, t2, t3 = var('x, y, z, a, b, c, t1, t2, t3') +sage: solve([ +....: x+a*t1 == 320870677764563-40*t1, y+b*t1 == 335750934489987-24*t1, z+c*t1 == 282502845957937+10*t1, +....: x+a*t2 == 219235623600942+127*t2, y+b*t2 == 408022798608755-45*t2, z+c*t2 == 245679379684914+66*t2, +....: x+a*t3 == 171834827764229-122*t3, y+b*t3 == 225154401936948-521*t3, z+c*t3 == 232302441670972+95*t3], +....: x,y,z,a,b,c,t1,t2,t3) +[[x == 149412455352770, y == 174964385672289, z == 233413147425100, a == 201, b == 202, c == 79, t1 == 711444906273, t2 == 943556327678, t3 == 69419109633]] +sage: 149412455352770+174964385672289+233413147425100 +557789988450159