flipflop3.py

FLIP = 7
FLOP = 8

print("Player Count\tMinimum N for all to play")
for player_count in range(1, 100000):
    got_to_play = set()
    direction = 1
    player = 0
    n = 0
    while len(got_to_play) < player_count:
        n += 1
        got_to_play.add(player)

        if n % FLIP == 0:
            direction = -direction
        if n % FLOP == 0:
            player += direction # skip 1 player

        player += direction
        player %= player_count

    print("{}\t{}".format(player_count, n))

gistfile1.txt

Player Count	Minimum N for all to play	Ratio
1	1	1
2	2	1
3	3	1
4	4	1
5	5	1
6	6	1
7	7	1
8	13	1.625
9	14	1.555555556
10	63	6.3
11	119	10.81818182
12	175	14.58333333
13	231	17.76923077
14	287	20.5
15	343	22.86666667
16	399	24.9375
17	455	26.76470588
18	511	28.38888889
19	567	29.84210526
20	623	31.15
21	679	32.33333333
22	735	33.40909091
23	791	34.39130435
24	847	35.29166667
25	903	36.12
26	959	36.88461538
27	1015	37.59259259
28	1071	38.25
29	1127	38.86206897
30	1183	39.43333333
31	1239	39.96774194
32	1295	40.46875
33	1351	40.93939394
34	1407	41.38235294
35	1463	41.8
36	1519	42.19444444
37	1575	42.56756757
38	1631	42.92105263
39	1687	43.25641026
40	1743	43.575
41	1799	43.87804878
42	1855	44.16666667
43	1911	44.44186047
44	1967	44.70454545
45	2023	44.95555556
46	2079	45.19565217
47	2135	45.42553191
48	2191	45.64583333
49	2247	45.85714286
50	2303	46.06
51	2359	46.25490196
52	2415	46.44230769
53	2471	46.62264151
54	2527	46.7962963
55	2583	46.96363636
56	2639	47.125
57	2695	47.28070175
58	2751	47.43103448
59	2807	47.57627119
60	2863	47.71666667
61	2919	47.85245902
62	2975	47.98387097
63	3031	48.11111111
64	3087	48.234375
65	3143	48.35384615
66	3199	48.46969697
67	3255	48.58208955
68	3311	48.69117647
69	3367	48.79710145
70	3423	48.9
71	3479	49
72	3535	49.09722222
73	3591	49.19178082
74	3647	49.28378378
75	3703	49.37333333
76	3759	49.46052632
77	3815	49.54545455
78	3871	49.62820513
79	3927	49.70886076
80	3983	49.7875
81	4039	49.86419753
82	4095	49.93902439
83	4151	50.01204819
84	4207	50.08333333
85	4263	50.15294118
86	4319	50.22093023
87	4375	50.28735632
88	4431	50.35227273
89	4487	50.41573034
90	4543	50.47777778
91	4599	50.53846154
92	4655	50.59782609
93	4711	50.65591398
94	4767	50.71276596
95	4823	50.76842105
96	4879	50.82291667
97	4935	50.87628866
98	4991	50.92857143
99	5047	50.97979798
100	5103	51.03
101	5159	51.07920792
102	5215	51.12745098
103	5271	51.17475728
104	5327	51.22115385
105	5383	51.26666667
106	5439	51.31132075
107	5495	51.35514019
108	5551	51.39814815
109	5607	51.44036697
110	5663	51.48181818
111	5719	51.52252252
112	5775	51.5625
113	5831	51.60176991
114	5887	51.64035088
115	5943	51.67826087
116	5999	51.71551724
117	6055	51.75213675
118	6111	51.78813559
119	6167	51.82352941
120	6223	51.85833333
121	6279	51.89256198
122	6335	51.92622951
123	6391	51.95934959
124	6447	51.99193548
125	6503	52.024
126	6559	52.05555556
127	6615	52.08661417
128	6671	52.1171875
129	6727	52.14728682
130	6783	52.17692308
131	6839	52.20610687
132	6895	52.23484848
133	6951	52.26315789
134	7007	52.29104478
135	7063	52.31851852
136	7119	52.34558824
137	7175	52.37226277
138	7231	52.39855072
139	7287	52.42446043
140	7343	52.45
141	7399	52.4751773
142	7455	52.5
143	7511	52.52447552
144	7567	52.54861111
145	7623	52.57241379
146	7679	52.59589041
147	7735	52.61904762
148	7791	52.64189189
149	7847	52.66442953
150	7903	52.68666667
151	7959	52.70860927
152	8015	52.73026316
153	8071	52.75163399
154	8127	52.77272727
155	8183	52.79354839
156	8239	52.81410256
157	8295	52.8343949
158	8351	52.85443038
159	8407	52.87421384
160	8463	52.89375
161	8519	52.91304348
162	8575	52.93209877
163	8631	52.95092025
164	8687	52.9695122
165	8743	52.98787879
166	8799	53.0060241
167	8855	53.0239521
168	8911	53.04166667
169	8967	53.0591716
170	9023	53.07647059
171	9079	53.09356725
172	9135	53.11046512
173	9191	53.12716763
174	9247	53.14367816
175	9303	53.16
176	9359	53.17613636
177	9415	53.1920904
178	9471	53.20786517
179	9527	53.22346369
180	9583	53.23888889
181	9639	53.25414365
182	9695	53.26923077
183	9751	53.28415301
184	9807	53.29891304
185	9863	53.31351351
186	9919	53.32795699
187	9975	53.34224599
188	10031	53.35638298
189	10087	53.37037037
190	10143	53.38421053
191	10199	53.39790576
192	10255	53.41145833
193	10311	53.42487047
194	10367	53.43814433
195	10423	53.45128205
196	10479	53.46428571
197	10535	53.47715736
198	10591	53.48989899
199	10647	53.50251256
200	10703	53.515
201	10759	53.52736318
202	10815	53.53960396
203	10871	53.55172414
204	10927	53.56372549
205	10983	53.57560976
206	11039	53.58737864
207	11095	53.59903382
208	11151	53.61057692
209	11207	53.62200957
210	11263	53.63333333
211	11319	53.64454976
212	11375	53.65566038
213	11431	53.66666667
214	11487	53.67757009
215	11543	53.68837209
216	11599	53.69907407
217	11655	53.70967742
218	11711	53.72018349
219	11767	53.73059361
220	11823	53.74090909
221	11879	53.75113122
222	11935	53.76126126
223	11991	53.77130045
224	12047	53.78125
225	12103	53.79111111
226	12159	53.80088496
227	12215	53.81057269
228	12271	53.82017544
229	12327	53.82969432
230	12383	53.83913043
231	12439	53.84848485
232	12495	53.85775862
233	12551	53.86695279
234	12607	53.87606838
235	12663	53.88510638
236	12719	53.8940678
237	12775	53.90295359
238	12831	53.91176471
239	12887	53.92050209
240	12943	53.92916667
241	12999	53.93775934
242	13055	53.94628099
243	13111	53.95473251
244	13167	53.96311475
245	13223	53.97142857
246	13279	53.9796748
247	13335	53.98785425
248	13391	53.99596774
249	13447	54.00401606
250	13503	54.012
251	13559	54.01992032
252	13615	54.02777778
253	13671	54.03557312
254	13727	54.04330709
255	13783	54.05098039
256	13839	54.05859375
257	13895	54.06614786
258	13951	54.07364341
259	14007	54.08108108
260	14063	54.08846154
261	14119	54.09578544
262	14175	54.10305344
263	14231	54.11026616
264	14287	54.11742424
265	14343	54.1245283
266	14399	54.13157895
267	14455	54.13857678
268	14511	54.14552239
269	14567	54.15241636
270	14623	54.15925926
271	14679	54.16605166
272	14735	54.17279412
273	14791	54.17948718
274	14847	54.18613139
275	14903	54.19272727
276	14959	54.19927536
277	15015	54.20577617
278	15071	54.21223022
279	15127	54.21863799
280	15183	54.225
281	15239	54.23131673
282	15295	54.23758865
283	15351	54.24381625
284	15407	54.25
285	15463	54.25614035
286	15519	54.26223776
287	15575	54.26829268
288	15631	54.27430556
289	15687	54.28027682
290	15743	54.2862069
291	15799	54.29209622
292	15855	54.29794521
293	15911	54.30375427
294	15967	54.30952381
295	16023	54.31525424
296	16079	54.32094595
297	16135	54.32659933
298	16191	54.33221477
299	16247	54.33779264
300	16303	54.34333333
301	16359	54.34883721
302	16415	54.35430464
303	16471	54.35973597
304	16527	54.36513158
305	16583	54.3704918
306	16639	54.37581699
307	16695	54.38110749
308	16751	54.38636364
309	16807	54.39158576
310	16863	54.39677419
311	16919	54.40192926
312	16975	54.40705128
313	17031	54.41214058
314	17087	54.41719745
315	17143	54.42222222
316	17199	54.42721519
317	17255	54.43217666
318	17311	54.43710692
319	17367	54.44200627
320	17423	54.446875
321	17479	54.4517134
322	17535	54.45652174
323	17591	54.46130031
324	17647	54.46604938
325	17703	54.47076923
326	17759	54.47546012
327	17815	54.48012232
328	17871	54.4847561
329	17927	54.4893617
330	17983	54.49393939
331	18039	54.49848943
332	18095	54.50301205
333	18151	54.50750751
334	18207	54.51197605
335	18263	54.51641791
336	18319	54.52083333
337	18375	54.52522255
338	18431	54.5295858
339	18487	54.5339233
340	18543	54.53823529
341	18599	54.54252199
342	18655	54.54678363
343	18711	54.55102041
344	18767	54.55523256
345	18823	54.55942029
346	18879	54.56358382
347	18935	54.56772334
348	18991	54.57183908
349	19047	54.57593123
350	19103	54.58
351	19159	54.58404558
352	19215	54.58806818
353	19271	54.59206799
354	19327	54.5960452
355	19383	54.6
356	19439	54.60393258
357	19495	54.60784314
358	19551	54.61173184
359	19607	54.61559889
360	19663	54.61944444
361	19719	54.6232687
362	19775	54.62707182
363	19831	54.63085399
364	19887	54.63461538
365	19943	54.63835616
366	19999	54.6420765
367	20055	54.64577657
368	20111	54.64945652
369	20167	54.65311653
370	20223	54.65675676
371	20279	54.66037736
372	20335	54.66397849
373	20391	54.66756032
374	20447	54.67112299
375	20503	54.67466667
376	20559	54.67819149
377	20615	54.68169761
378	20671	54.68518519
379	20727	54.68865435
380	20783	54.69210526
381	20839	54.69553806
382	20895	54.69895288
383	20951	54.70234987
384	21007	54.70572917
385	21063	54.70909091
386	21119	54.71243523
387	21175	54.71576227
388	21231	54.71907216
389	21287	54.72236504
390	21343	54.72564103
391	21399	54.72890026
392	21455	54.73214286
393	21511	54.73536896
394	21567	54.73857868
395	21623	54.74177215
396	21679	54.74494949
397	21735	54.74811083
398	21791	54.75125628
399	21847	54.75438596
400	21903	54.7575
401	21959	54.7605985
402	22015	54.76368159
403	22071	54.76674938
404	22127	54.76980198
405	22183	54.77283951
406	22239	54.77586207
407	22295	54.77886978
408	22351	54.78186275
409	22407	54.78484108
410	22463	54.78780488
411	22519	54.79075426
412	22575	54.79368932
413	22631	54.79661017
414	22687	54.79951691
415	22743	54.80240964
416	22799	54.80528846
417	22855	54.80815348
418	22911	54.81100478
419	22967	54.81384248
420	23023	54.81666667
421	23079	54.81947743
422	23135	54.82227488
423	23191	54.8250591
424	23247	54.82783019
425	23303	54.83058824
426	23359	54.83333333
427	23415	54.83606557
428	23471	54.83878505
429	23527	54.84149184
430	23583	54.84418605
431	23639	54.84686775
432	23695	54.84953704
433	23751	54.852194
434	23807	54.85483871
435	23863	54.85747126
436	23919	54.86009174
437	23975	54.86270023
438	24031	54.8652968
439	24087	54.86788155
440	24143	54.87045455
441	24199	54.87301587
442	24255	54.87556561
443	24311	54.87810384
444	24367	54.88063063
445	24423	54.88314607
446	24479	54.88565022
447	24535	54.88814318
448	24591	54.890625
449	24647	54.89309577
450	24703	54.89555556
451	24759	54.89800443
452	24815	54.90044248
453	24871	54.90286976
454	24927	54.90528634
455	24983	54.90769231
456	25039	54.91008772
457	25095	54.91247265
458	25151	54.91484716
459	25207	54.91721133
460	25263	54.91956522
461	25319	54.92190889
462	25375	54.92424242
463	25431	54.92656587
464	25487	54.92887931
465	25543	54.9311828
466	25599	54.93347639
467	25655	54.93576017
468	25711	54.93803419
469	25767	54.94029851
470	25823	54.94255319
471	25879	54.9447983
472	25935	54.9470339
473	25991	54.94926004
474	26047	54.95147679
475	26103	54.95368421
476	26159	54.95588235
477	26215	54.95807128
478	26271	54.96025105
479	26327	54.96242171
480	26383	54.96458333
481	26439	54.96673597
482	26495	54.96887967
483	26551	54.97101449
484	26607	54.9731405
485	26663	54.97525773
486	26719	54.97736626
487	26775	54.97946612
488	26831	54.98155738
489	26887	54.98364008
490	26943	54.98571429
491	26999	54.98778004
492	27055	54.9898374
493	27111	54.99188641
494	27167	54.99392713
495	27223	54.9959596
496	27279	54.99798387
497	27335	55
498	27391	55.00200803
499	27447	55.00400802
500	27503	55.006
501	27559	55.00798403
502	27615	55.00996016
503	27671	55.01192843
504	27727	55.01388889
505	27783	55.01584158
506	27839	55.01778656
507	27895	55.01972387
508	27951	55.02165354
509	28007	55.02357564
510	28063	55.0254902
511	28119	55.02739726
512	28175	55.02929688
513	28231	55.03118908
514	28287	55.03307393
515	28343	55.03495146
516	28399	55.03682171
517	28455	55.03868472
518	28511	55.04054054
519	28567	55.04238921
520	28623	55.04423077
521	28679	55.04606526
522	28735	55.04789272
523	28791	55.04971319
524	28847	55.05152672
525	28903	55.05333333
526	28959	55.05513308
527	29015	55.056926
528	29071	55.05871212
529	29127	55.06049149
530	29183	55.06226415
531	29239	55.06403013
532	29295	55.06578947
533	29351	55.06754221
534	29407	55.06928839
535	29463	55.07102804
536	29519	55.07276119
537	29575	55.0744879
538	29631	55.07620818
539	29687	55.07792208
540	29743	55.07962963
541	29799	55.08133087
542	29855	55.08302583
543	29911	55.08471455
544	29967	55.08639706
545	30023	55.08807339
546	30079	55.08974359
547	30135	55.09140768
548	30191	55.09306569
549	30247	55.09471767
550	30303	55.09636364
551	30359	55.09800363
552	30415	55.09963768
553	30471	55.10126582
554	30527	55.10288809
555	30583	55.1045045
556	30639	55.10611511
557	30695	55.10771993
558	30751	55.109319
559	30807	55.11091234
560	30863	55.1125
561	30919	55.114082
562	30975	55.11565836