Problem 397

[mctrafik]

Can someone post working a, b, c as an example? Or better yet the 41 of them for the case F(1, 10). For some reason I get 67 and don't know which ones are wrong. I double-checked my math and it seems solid.

Here are the numbers I get (a, b, c, k):

-10 -9 10 1
-10 9 10 1
-9 -8 9 1
-9 8 9 1
-9 9 10 1
-10 -9 9 1
-8 -7 8 1
-8 5 10 1
-10 -5 8 1
-8 7 8 1
-8 8 9 1
-9 -8 8 1
-7 -6 7 1
-7 4 9 1
-9 -4 7 1
-7 5 10 1
-10 -5 7 1
-7 6 7 1
-7 7 8 1
-8 -7 7 1
-6 -5 6 1
-6 3 8 1
-8 -3 6 1
-6 4 9 1
-9 -4 6 1
-6 5 6 1
-6 6 7 1
-7 -6 6 1
-5 -4 5 1
-5 2 7 1
-7 -2 5 1
-5 3 8 1
-8 -3 5 1
-5 4 5 1
-5 5 6 1
-6 -5 5 1
-4 -3 4 1
-4 1 6 1
-6 -1 4 1
-4 2 7 1
-7 -2 4 1
-4 3 4 1
-4 4 5 1
-5 -4 4 1
-3 -2 3 1
-3 0 5 1
-5 0 3 1
-3 1 6 1
-6 -1 3 1
-3 2 3 1
-3 3 4 1
-4 -3 3 1
-2 -1 2 1
-2 -1 3 1
-3 1 2 1
-2 -1 4 1
-4 1 2 1
-2 0 3 1
-3 0 2 1
-2 0 5 1
-5 0 2 1
-2 1 2 1
-2 2 3 1
-3 -2 2 1
-1 0 1 1
-1 1 2 1
-2 -1 1 1

[luckyrodman]

Well, this forum is used for clarifications when you don't understand the statement of the problem.

It's not used for discussing the solution.

If you want to discuss the solution, I think you have a place to discuss with, haven't you? kifart

[ffff0]

I've sent a PM with a list.

[mctrafik]

I've sent a PM with a list.

Thank you so much.

@LuckyRod
Also this was a clarification question. I'm pretty sure the challenge of the question is not checking for a 45-degree angle.

[mihassan]

I am also getting 67 set of values instead of 41. What am I missing?

[stimmer]

Be assured that there really are just 41 triangles with a 45-degree angle for k=1. Without giving anything away, the next step is to use common sense - look at the list of triangle coordinates your code made, do some of them feel like they wouldn't have a 45 degree angle? Try sketcking some on graph paper, or get your computer to draw them.

[mihassan]

Thanks. Got it now.

[noonie12]

Alright... I've been working on this for a while and I can't seem to get it. Would you mind pm-ing me the list. For some reason I'm getting 130 results, which is even worse than what the OP was getting!

*K = 1: A: (-10, 100) + B: (-9, 81) + C: (9, 81)
*K = 1: A: (-9, 81) + B: (-8, 64) + C: (8, 64)
*K = 1: A: (-9, 81) + B: (-8, 64) + C: (9, 81)
*K = 1: A: (-9, 81) + B: (8, 64) + C: (-8, 64)
*K = 1: A: (-9, 81) + B: (8, 64) + C: (9, 81)
*K = 1: A: (-9, 81) + B: (9, 81) + C: (-8, 64)
*K = 1: A: (-9, 81) + B: (9, 81) + C: (8, 64)
*K = 1: A: (-9, 81) + B: (9, 81) + C: (10, 100)
*K = 1: A: (-8, 64) + B: (-9, 81) + C: (8, 64)
*K = 1: A: (-8, 64) + B: (-9, 81) + C: (9, 81)
*K = 1: A: (-8, 64) + B: (-7, 49) + C: (8, 64)
*K = 1: A: (-8, 64) + B: (7, 49) + C: (8, 64)
*K = 1: A: (-8, 64) + B: (8, 64) + C: (-7, 49)
*K = 1: A: (-8, 64) + B: (8, 64) + C: (7, 49)
*K = 1: A: (-8, 64) + B: (8, 64) + C: (9, 81)
*K = 1: A: (-8, 64) + B: (9, 81) + C: (8, 64)
*K = 1: A: (-7, 49) + B: (-8, 64) + C: (8, 64)
*K = 1: A: (-7, 49) + B: (8, 64) + C: (-8, 64)
*K = 1: A: (-6, 36) + B: (-5, 25) + C: (5, 25)
*K = 1: A: (-6, 36) + B: (5, 25) + C: (-5, 25)
*K = 1: A: (-5, 25) + B: (-6, 36) + C: (5, 25)
*K = 1: A: (-5, 25) + B: (-4, 16) + C: (4, 16)
*K = 1: A: (-5, 25) + B: (-4, 16) + C: (5, 25)
*K = 1: A: (-5, 25) + B: (4, 16) + C: (-4, 16)
*K = 1: A: (-5, 25) + B: (4, 16) + C: (5, 25)
*K = 1: A: (-5, 25) + B: (5, 25) + C: (-6, 36)
*K = 1: A: (-5, 25) + B: (5, 25) + C: (-4, 16)
*K = 1: A: (-5, 25) + B: (5, 25) + C: (4, 16)
*K = 1: A: (-5, 25) + B: (5, 25) + C: (6, 36)
*K = 1: A: (-5, 25) + B: (6, 36) + C: (5, 25)
*K = 1: A: (-4, 16) + B: (-5, 25) + C: (4, 16)
*K = 1: A: (-4, 16) + B: (-5, 25) + C: (5, 25)
*K = 1: A: (-4, 16) + B: (-3, 9) + C: (3, 9)
*K = 1: A: (-4, 16) + B: (-3, 9) + C: (4, 16)
*K = 1: A: (-4, 16) + B: (3, 9) + C: (-3, 9)
*K = 1: A: (-4, 16) + B: (3, 9) + C: (4, 16)
*K = 1: A: (-4, 16) + B: (4, 16) + C: (-5, 25)
*K = 1: A: (-4, 16) + B: (4, 16) + C: (-3, 9)
*K = 1: A: (-4, 16) + B: (4, 16) + C: (3, 9)
*K = 1: A: (-4, 16) + B: (4, 16) + C: (5, 25)
*K = 1: A: (-4, 16) + B: (5, 25) + C: (-5, 25)
*K = 1: A: (-4, 16) + B: (5, 25) + C: (4, 16)
*K = 1: A: (-3, 9) + B: (-4, 16) + C: (3, 9)
*K = 1: A: (-3, 9) + B: (-4, 16) + C: (4, 16)
*K = 1: A: (-3, 9) + B: (-2, 4) + C: (2, 4)
*K = 1: A: (-3, 9) + B: (-2, 4) + C: (3, 9)
*K = 1: A: (-3, 9) + B: (2, 4) + C: (-2, 4)
*K = 1: A: (-3, 9) + B: (2, 4) + C: (3, 9)
*K = 1: A: (-3, 9) + B: (3, 9) + C: (-4, 16)
*K = 1: A: (-3, 9) + B: (3, 9) + C: (-2, 4)
*K = 1: A: (-3, 9) + B: (3, 9) + C: (2, 4)
*K = 1: A: (-3, 9) + B: (3, 9) + C: (4, 16)
*K = 1: A: (-3, 9) + B: (4, 16) + C: (-4, 16)
*K = 1: A: (-3, 9) + B: (4, 16) + C: (3, 9)
*K = 1: A: (-2, 4) + B: (-3, 9) + C: (2, 4)
*K = 1: A: (-2, 4) + B: (-3, 9) + C: (3, 9)
*K = 1: A: (-2, 4) + B: (-1, 1) + C: (2, 4)
*K = 1: A: (-2, 4) + B: (1, 1) + C: (2, 4)
*K = 1: A: (-2, 4) + B: (2, 4) + C: (-3, 9)
*K = 1: A: (-2, 4) + B: (2, 4) + C: (-1, 1)
*K = 1: A: (-2, 4) + B: (2, 4) + C: (1, 1)
*K = 1: A: (-2, 4) + B: (2, 4) + C: (3, 9)
*K = 1: A: (-2, 4) + B: (3, 9) + C: (-3, 9)
*K = 1: A: (-2, 4) + B: (3, 9) + C: (2, 4)
*K = 1: A: (-1, 1) + B: (-2, 4) + C: (2, 4)
*K = 1: A: (-1, 1) + B: (0, 0) + C: (1, 1)
*K = 1: A: (-1, 1) + B: (1, 1) + C: (0, 0)
*K = 1: A: (-1, 1) + B: (2, 4) + C: (-2, 4)
*K = 1: A: (0, 0) + B: (-1, 1) + C: (1, 1)
*K = 1: A: (0, 0) + B: (1, 1) + C: (-1, 1)
*K = 1: A: (1, 1) + B: (-2, 4) + C: (2, 4)
*K = 1: A: (1, 1) + B: (-1, 1) + C: (0, 0)
*K = 1: A: (1, 1) + B: (0, 0) + C: (-1, 1)
*K = 1: A: (1, 1) + B: (2, 4) + C: (-2, 4)
*K = 1: A: (2, 4) + B: (-3, 9) + C: (-2, 4)
*K = 1: A: (2, 4) + B: (-3, 9) + C: (3, 9)
*K = 1: A: (2, 4) + B: (-2, 4) + C: (-3, 9)
*K = 1: A: (2, 4) + B: (-2, 4) + C: (-1, 1)
*K = 1: A: (2, 4) + B: (-2, 4) + C: (1, 1)
*K = 1: A: (2, 4) + B: (-2, 4) + C: (3, 9)
*K = 1: A: (2, 4) + B: (-1, 1) + C: (-2, 4)
*K = 1: A: (2, 4) + B: (1, 1) + C: (-2, 4)
*K = 1: A: (2, 4) + B: (3, 9) + C: (-3, 9)
*K = 1: A: (2, 4) + B: (3, 9) + C: (-2, 4)
*K = 1: A: (3, 9) + B: (-4, 16) + C: (-3, 9)
*K = 1: A: (3, 9) + B: (-4, 16) + C: (4, 16)
*K = 1: A: (3, 9) + B: (-3, 9) + C: (-4, 16)
*K = 1: A: (3, 9) + B: (-3, 9) + C: (-2, 4)
*K = 1: A: (3, 9) + B: (-3, 9) + C: (2, 4)
*K = 1: A: (3, 9) + B: (-3, 9) + C: (4, 16)
*K = 1: A: (3, 9) + B: (-2, 4) + C: (-3, 9)
*K = 1: A: (3, 9) + B: (-2, 4) + C: (2, 4)
*K = 1: A: (3, 9) + B: (2, 4) + C: (-3, 9)
*K = 1: A: (3, 9) + B: (2, 4) + C: (-2, 4)
*K = 1: A: (3, 9) + B: (4, 16) + C: (-4, 16)
*K = 1: A: (3, 9) + B: (4, 16) + C: (-3, 9)
*K = 1: A: (4, 16) + B: (-5, 25) + C: (-4, 16)
*K = 1: A: (4, 16) + B: (-5, 25) + C: (5, 25)
*K = 1: A: (4, 16) + B: (-4, 16) + C: (-5, 25)
*K = 1: A: (4, 16) + B: (-4, 16) + C: (-3, 9)
*K = 1: A: (4, 16) + B: (-4, 16) + C: (3, 9)
*K = 1: A: (4, 16) + B: (-4, 16) + C: (5, 25)
*K = 1: A: (4, 16) + B: (-3, 9) + C: (-4, 16)
*K = 1: A: (4, 16) + B: (-3, 9) + C: (3, 9)
*K = 1: A: (4, 16) + B: (3, 9) + C: (-4, 16)
*K = 1: A: (4, 16) + B: (3, 9) + C: (-3, 9)
*K = 1: A: (4, 16) + B: (5, 25) + C: (-5, 25)
*K = 1: A: (4, 16) + B: (5, 25) + C: (-4, 16)
*K = 1: A: (5, 25) + B: (-6, 36) + C: (-5, 25)
*K = 1: A: (5, 25) + B: (-5, 25) + C: (-6, 36)
*K = 1: A: (5, 25) + B: (-5, 25) + C: (-4, 16)
*K = 1: A: (5, 25) + B: (-5, 25) + C: (4, 16)
*K = 1: A: (5, 25) + B: (-5, 25) + C: (6, 36)
*K = 1: A: (5, 25) + B: (-4, 16) + C: (-5, 25)
*K = 1: A: (5, 25) + B: (-4, 16) + C: (4, 16)
*K = 1: A: (5, 25) + B: (4, 16) + C: (-5, 25)
*K = 1: A: (5, 25) + B: (4, 16) + C: (-4, 16)
*K = 1: A: (5, 25) + B: (6, 36) + C: (-5, 25)
*K = 1: A: (6, 36) + B: (-5, 25) + C: (5, 25)
*K = 1: A: (6, 36) + B: (5, 25) + C: (-5, 25)
*K = 1: A: (7, 49) + B: (-8, 64) + C: (8, 64)
*K = 1: A: (7, 49) + B: (8, 64) + C: (-8, 64)
*K = 1: A: (8, 64) + B: (-9, 81) + C: (-8, 64)
*K = 1: A: (8, 64) + B: (-9, 81) + C: (9, 81)
*K = 1: A: (8, 64) + B: (-8, 64) + C: (-7, 49)
*K = 1: A: (8, 64) + B: (-8, 64) + C: (7, 49)
*K = 1: A: (8, 64) + B: (-8, 64) + C: (9, 81)
*K = 1: A: (8, 64) + B: (-7, 49) + C: (-8, 64)
*K = 1: A: (8, 64) + B: (7, 49) + C: (-8, 64)
*K = 1: A: (8, 64) + B: (9, 81) + C: (-8, 64)

I'm using the pythagorean and law of cosines, as that's all I've really learned in math class/come across on the internet. Any advice would be much appreciated, and if you could PM your list for the 41 numbers that would be awesome!

[hk]

Aren't
*K = 1: A: (-9, 81) + B: (-8, 64) + C: (8, 64)
and
*K = 1: A: (-8, 64) + B: (-9, 81) + C: (8, 64)
the same triple?