Newtonian Bowling

[freeztar]

Building off Jay-qu's results:
position (4,2)
velocity (.13,1.5)

[CraigD]

Originally Posted by freeztar

Building off Jay-qu's results:
position (4,2)
velocity (.13,1.5)

Leaves the 3, 4, 6, 7, and 10 pins:

   c                               d
 
               f
 
 
 
 
 
                   1
 
               2       3
 
           4       5       6
 
       7       8       9       a
 
   e
Sim T:0

   c                               d
 
 
 
 
 
 
                f
                   1
 
               2       3
 
           4       5       6
 
       7       8       9       a
 
   e
Sim T:1.950928691036618315

   c                               d
 
 
 
 
 
 
 
                f  1
 
              2        3
 
           4       5       6
 
       7       8       9       a
 
   e
Sim T:2.197907995854913325

   c                               d
 
 
 
 
 
 
 
                     1
 
                 f     3
 
           4       5       6
 
       7       8       9       a
           2
   e
Sim T:3.532699333660073598

   c                               d
 
 
 
 
 
 
 
                     1
 
                 f     3
 
           4       5       6
 
       7       8       9       a
 
   e
Sim T:3.711481229400547556

   c                               d
 
 
 
 
 
 
 
                      1
 
                       3
                 f
           4               6
                     5
       7       8       9       a
 
   e
Sim T:4.320681805059865239

   c                               d
 
 
 
 
 
 
 
                         1
 
                       3
 
           4     f         6
 
       7      8    5           a
                            9
   e
Sim T:5.677890374760305092

   c                               d
 
 
 
 
 
 
 
                          1
 
                       3
 
           4               6
                 f
       7      8                a
                   5
   e
Sim T:6.257024212402047323

   c                               d
 
 
 
 
 
 
 
                           1
 
                       3
 
           4               6
 
       7         f             a
            8
   e
Sim T:7.067046335083775568

   c                               d
 
 
 
 
 
 
 
                             1
 
                       3
 
           4               6
 
       7          f            a
 
   e
Sim T:8.336194591971233124

   c                               d
 
 
 
 
 
 
 
                               1
 
                       3
 
           4               6
 
       7                       a
 
   e
Sim T:9.7114979906330351

   c                               d
 
 
 
 
 
 
 
 
 
                       3
 
           4               6
 
       7                       a
 
   e
Sim T:100.1891241304918385

[freeztar]

Originally Posted by CraigD

Leaves the 3, 4, 6, 7, and 10 pins

This is too cool Craig! I love scrolling the ASCII!

Next ball:

x=5.1
v=(.01,2)

I don't think I could bowl if we didn't have uniform acceleration. It's quite challenging already. (especially without the MUMPS)

[Jay-qu]

Originally Posted by freeztar

Building off Jay-qu's results:
position (4,2)
velocity (.13,1.5)

building ey? you went backwards

Ill wait for the results of the your last one before making the next guess

[CraigD]

Originally Posted by freeztar

Next ball:

x=5.1
v=(.01,2)

Left the 2, 7, and 8.

   c                               d
 
                   f
 
 
 
 
 
                   1
 
               2       3
 
           4       5       6
 
       7       8       9       a
 
   e
Sim T:0

   c                               d
 
 
 
 
 
                   f
 
                  1
 
               2       3
 
           4       5       6
 
       7       8       9       a
 
   e
Sim T:1.129151581334108686

   c                               d
 
 
 
 
 
 
                   f
 
 
               2       3
                  1
           4       5       6
 
       7       8       9       a
 
   e
Sim T:1.660583098910104342

   c                               d
 
 
 
 
 
 
 
                    f
 
               2       3
               1
           4               6
                     5
       7       8       9       a
 
   e
Sim T:2.111042843782550941

   c                               d
 
 
 
 
 
 
 
 
                    f
               2       3
 
           41              6
 
       7       8         9     a
                    5
   e
Sim T:2.507936633072608453

   c                               d
 
 
 
 
 
 
 
 
                    f
               2       3
          4
            1              6
 
       7       8         9     a
                    5
   e
Sim T:2.525317322457848671

   c                               d
 
 
 
 
 
 
 
 
                    f
               2       3
          4
            1              6
 
       7       8         9     a
 
   e
Sim T:2.642141732752977068

   c                               d
 
 
 
 
 
 
 
 
 
               2   f     3
        4
                           6
                               a
       7  1    8             9
 
   e
Sim T:3.270748603422506357

   c                               d
 
 
 
 
 
 
 
 
 
       4       2
                   f       3
                           6
                                 a
       7       8             9
        1
   e
Sim T:3.780938409812005104

   c                               d
 
 
 
 
 
 
 
 
 
       4       2
                   f       3
                          6
                                 a
       7       8             9
 
   e
Sim T:3.866924101807587732

   c                               d
 
 
 
 
 
 
 
 
 
      4        2
                            3
                   f      6
 
       7       8
                             9
   e
Sim T:4.138466973406817131

   c                               d
 
 
 
 
 
 
 
 
   4
               2
                              3
                          6
                   f
       7       8
 
   e
Sim T:4.955453089700254796

   c                               d
 
 
 
 
 
 
 
 
 
               2
                               3
 
                          6
       7       8   f
 
   e
Sim T:5.26440506719893168

   c                               d
 
 
 
 
 
 
 
 
 
               2
 
 
                          6
       7       8
                  f
   e
Sim T:6.236267419670890565

   c                               d
 
 
 
 
 
 
 
 
 
               2
 
 
                          6
       7       8
 
   e
Sim T:6.243812159622428016

   c                               d
 
 
 
 
 
 
 
 
 
               2
 
 
 
       7       8
 
   e
Sim T:9.206268540570421616

[Jay-qu]

I would like to use the low mass ball, 1.75
position - (4.5,2)
velocity - (.2,3)

[CraigD]

Originally Posted by Jay-qu

I would like to use the low mass ball, 1.75
position - (4.5,2)
velocity - (.2,3)

Left the 7 and 10 pins. Notice that the lighter ball exited via the left gutter, not the usual back one:

   c                               d
 
                 f
 
 
 
 
 
                   1
 
               2       3
 
           4       5       6
 
       7       8       9       a
 
   e
Sim T:0

   c                               d
 
 
 
 
 
                 f
 
                   1
 
               2       3
 
           4       5       6
 
       7       8       9       a
 
   e
Sim T:.777919545042750755

   c                               d
 
 
 
 
 
 
                f
 
                     1
               2       3
 
           4       5       6
 
       7       8       9       a
 
   e
Sim T:1.088831401225141388

   c                               d
 
 
 
 
 
 
 
               f
 
               2        3
                    1
           4      5        6
 
       7       8       9       a
 
   e
Sim T:1.359682199698044096

   c                               d
 
 
 
 
 
 
 
               f
 
              2           3
 
           4      5  1     6
 
       7       8       9       a
 
   e
Sim T:1.536127986081857928

   c                               d
 
 
 
 
 
 
 
               f
 
              2            3
 
           4     5         6
                      1
       7       8       9       a
 
   e
Sim T:1.67789928576067876

   c                               d
 
 
 
 
 
 
 
              f
 
                              3
              2
           4   5           6
                      1
       7       8               a
 
   e
Sim T:2.089191257551762255

   c                               d
 
 
 
 
 
 
 
              f
 
                              3
 
           4  2            6
              5       1
       7       8               a
 
   e
Sim T:2.145426340628022034

   c                               d
 
 
 
 
 
 
 
              f
 
                              3
 
           4  2            6
              5       1
       7       8               a
 
   e
Sim T:2.149602697649281967

   c                               d
 
 
 
 
 
 
 
              f
 
                              3
 
           4  2            6
              5       1
       7       8               a
 
   e
Sim T:2.151491758845930496

   c                               d
 
 
 
 
 
 
 
 
            f
                                  3
             2
           4          1    6
            5
       7                       a
 
   e
Sim T:2.740346050039052469

   c                               d
 
 
 
 
 
 
 
 
            f
                                  3
            2
          4           1    6
            5
       7                       a
 
   e
Sim T:2.741579721949027997

   c                               d
 
 
 
 
 
 
 
 
            f
 
            2
          4           1    6
            5
       7                       a
 
   e
Sim T:2.757726307339755415

   c                               d
 
 
 
 
 
 
 
 
 
        f
            2
      4                 1  6
 
       7                       a
 
   e
Sim T:4.480659557197903538

   c                               d
 
 
 
 
 
 
 
 
 
     f
            2
   4                    1  6
 
       7                       a
 
   e
Sim T:5.831707787566365708

   c                               d
 
 
 
 
 
 
 
 
 
    f
            2
                         1 6
 
       7                       a
 
   e
Sim T:6.062693986860683766

   c                               d
 
 
 
 
 
 
 
 
 
 
    f       2
                         1 6
 
       7                       a
 
   e
Sim T:6.330721046784307345

   c                               d
 
 
 
 
 
 
 
 
 
 
            2              6
                         1
 
       7                       a
 
   e
Sim T:7.061848126602352592

   c                               d
 
 
 
 
 
 
 
 
            2
 
 
                         1
 
       7                       a
 
   e
Sim T:19.53002450574772863

            2
 
   c                               d
 
 
 
 
 
 
 
 
 
 
 
 
 
       7                       a
 
   e
Sim T:113.6839091067619267

   c                               d
 
 
 
 
 
 
 
 
 
 
 
 
 
       7                       a
 
   e
Sim T:1426.408598822751046

[freeztar]

Originally Posted by CraigD

Left the 7 and 10 pins. Notice that the lighter ball exited via the left gutter, not the usual back one:

...
Sim T:1426.408598822751046

Look at that sim time!
The next longest was only 31.xx!

Ok, I'll try again (and again and again I'm sure). Actually, I'd like to compare two different approaches this time.

1.
Ball mass=1.7
x=5.1
v=(.13,1.5)

2.
Ball mass=1.7
x=8
v=(.75,3)

[CraigD]

Originally Posted by freeztar

Look at that sim time!
The next longest was only 31.xx!

That is odd – looking at the internals, it appears that the event for the collision of the 2 with the top gutter got lost, due to a bug in the code!

OK, one ugly fix later (from an efficiency perspective – rather than restructure to prevent the bug, I added a few redundant calculations to fix it when it occurs – accuracy is unaffected), the gutter-skipping problem is fixed, so the sim time when the last pin collides with a gutter is about 113.68.

It’s past my bedtime. I’ll recheck the previous games tomorrow, and redo my statistics.

Ok, I'll try again (and again and again I'm sure). Actually, I'd like to compare two different approaches this time.

1.
Ball mass=1.7
x=5.1
v=(.13,1.5)

Left the 2, 4, 5, 6, and 10. (which emphasizes how unlike actual bowling with tall, skinny 3-d pins this game is, as this seems nearly impossible in that game):

   c                               d
 
                   f
 
 
 
 
 
                   1
 
               2       3
 
           4       5       6
 
       7       8       9       a
 
   e
Sim T:0

   c                               d
 
 
 
 
 
                    f
 
                  1
 
               2       3
 
           4       5       6
 
       7       8       9       a
 
   e
Sim T:1.541871524786457375

   c                               d
 
 
 
 
 
 
 
                       f
 
               2       3
 
           4  1    5       6
 
       7       8       9       a
 
   e
Sim T:3.11373549115469273

   c                               d
 
 
 
 
 
 
 
                       f
 
               2      3
 
           4       5       6
              1
       7       8       9       a
 
   e
Sim T:3.18672765140654457

   c                               d
 
 
 
 
 
 
 
                         f
 
               2
                      3
           4       5       6
           1
       7               9       a
 
   e
Sim T:3.932504301279100623

   c                               d
 
 
 
 
 
 
 
 
                           f
               2
 
           4       5  3    6
        1
      7                9       a
 
   e
Sim T:4.737356205666750719

   c                               d
 
 
 
 
 
 
 
 
                             f
               2
 
           4       5       6
        1            3
    7                  9       a
 
   e
Sim T:5.594343221034535679

   c                               d
 
 
 
 
 
 
 
 
                              f
               2
 
           4       5       6
        1            3
                       9       a
 
   e
Sim T:5.918824235004200073

   c                               d
 
 
 
 
 
 
 
 
 
               2                  f
 
       1   4       5       6
 
                  3            a
 
   e
Sim T:7.982483888007819619

   c                               d
 
 
 
 
 
 
 
 
 
               2
 
       1   4       5       6
 
                  3            a
 
   e
Sim T:8.046090915781519419

   c                               d
 
 
 
 
 
 
 
 
 
      1        2
 
           4       5       6
 
                               a
 
   e
Sim T:12.24047467539547201

   c                               d
 
 
 
 
 
 
 
 
 
               2
 
           4       5       6
 
                               a
 
   e
Sim T:39.90734327008380854

2.
Ball mass=1.7
x=8
v=(.75,3)

left all ten pins – a true “gutter ball”:

   c                               d
 
                               f
 
 
 
 
 
                   1
 
               2       3
 
           4       5       6
 
       7       8       9       a
 
   e
Sim T:0

   c                               d
 
 
 
 
 
 
 
                   1
                                  f
               2       3
 
           4       5       6
 
       7       8       9       a
 
   e
Sim T:1.25

   c                               d
 
 
 
 
 
 
 
                   1
 
               2       3
 
           4       5       6
 
       7       8       9       a
 
   e
Sim T:1.333333333333333343

[CraigD]

Originally Posted by CraigD

OK, one ugly fix later (from an efficiency perspective – rather than restructure to prevent the bug, I added a few redundant calculations to fix it when it occurs – accuracy is unaffected), the gutter-skipping problem is fixed, so the sim time when the last pin collides with a gutter is about 113.68.

It’s past my bedtime. I’ll recheck the previous games tomorrow, and redo my statistics.

I made an additional code change to un-uglify it, eliminating the redundant calculations, posted the fixed code were the unfixed appeared in post #1, and reran it for the previous contest submissions. Programmers luck smiles upon me, but with irony, and there were no differences in any previous results except for the example I gave in post #1, which I fixed.

So, after 8 days, we are still waiting for a first winner! To summarize the competition so far:
(example, doesn’t count): ball mass 3, x=1.5, (h,v)=(.87,1) -> 2 left: 4, 10
Jay-qu: ball mass 3, x=4, (h,v)=(.25,1.5) -> 2 left: 4, 7
chendoh: ball mass 3, x=1.5, (h,v)=(.86,1.3) -> 6 left: 1, 3, 4, 6, 7, 8
chendoh: ball mass 3, x=5.5, (h,v)=(.2,1) -> 6 left: 1, 2, 4, 5, 7, 8
Janus: ball mass 3, x=3.5, (h,v)=(.3,1) -> 5 left: 3, 4, 6, 7, 8
Jay-qu: ball mass 3, x=4, (h,v)=(.2,1.5) -> 3 left: 4, 7, 10
freeztar: ball mass 3, x=4, (h,v)=(.13,1.5) -> 5 left: 3, 4, 6, 7, 10
freeztar: ball mass 3, x=5.1, (h,v)=(.01,2) -> 3 left: 2, 7, 8
Jay-qu: ball mass 1.75, x=4.5, (h,v)=(.2,3) -> 2 left: 7, 10
freeztar: ball mass 1.7, x=5.1, (h,v)=(.13,1.5) -> 5 left: 2, 4, 5, 6, 10
freeztar: ball mass 1.7, x=8, (h,v)=(.75,3) -> 10 left: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10

So, YOU can still be the first to win this game of pure Newtonian mechanics – but only if you play. Bring your algebra and arithmetic, your iterative technique, dazzling intuition or blind luck, and play!