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Countdown.java
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README.md
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README.md

Best Countdown

In order to solve this, I just simulated millions of possible games to come up with probabilities.

I used the solver found at (https://www.cs.ox.ac.uk/admissions/undergraduate/courses/countdown.html)[https://www.cs.ox.ac.uk/admissions/undergraduate/courses/countdown.html] and wrote a simple python program to do the analysis.

For the first question:

What number of “large” cards is most likely to produce a solvable game and what number of “large” cards is least likely to be solvable?

I found:

# Bigs Solvable Games Games Played Success Rate
0 1329626 1585218 0.838765
1 1546962 1582761 0.977382
2 1555290 1583547 0.982156
3 1499468 1582761 0.947375
4 1434659 1585713 0.904741

Which implies that 2 big numbers are the best, with 98.2% of all boards being solvable followed by 1 big number (97.7%), 3 big numbers (94.7%), 4 big numbers (90.5%) and 0 big numbers (83.9%). This kinda makes sense, the big numbers can jump you to the upper hundreds where you can use the rest of your numbers fine tuning your answer.

For the second question:

What three-digit numbers are most or least likely to be solvable?

Full 3 Digit Table
target Solvable Games Games Played Success Rate
100 8572 8572 1
101 8842 8842 1
102 8877 8877 1
103 8777 8780 0.999658
104 8807 8808 0.999886
105 8790 8791 0.999886
106 8832 8833 0.999887
107 8657 8659 0.999769
108 8669 8669 1
109 8731 8742 0.998742
110 8753 8754 0.999886
111 8925 8926 0.999888
112 8815 8815 1
113 8792 8798 0.999318
114 8848 8848 1
115 8755 8757 0.999772
116 8723 8728 0.999427
117 8773 8777 0.999544
118 8687 8690 0.999655
119 8823 8834 0.998755
120 8599 8600 0.999884
121 8857 8857 1
122 8728 8736 0.999084
123 8793 8800 0.999205
124 8842 8844 0.999774
125 8764 8764 1
126 8771 8772 0.999886
127 8827 8829 0.999773
128 8655 8661 0.999307
129 8653 8654 0.999884
130 8717 8719 0.999771
131 8970 8981 0.998775
132 8883 8895 0.998651
133 8520 8525 0.999413
134 8791 8795 0.999545
135 8748 8753 0.999429
136 8828 8830 0.999773
137 8771 8795 0.997271
138 8759 8762 0.999658
139 8736 8745 0.998971
140 8806 8806 1
141 8743 8761 0.997945
142 8855 8861 0.999323
143 8728 8736 0.999084
144 8778 8779 0.999886
145 8776 8776 1
146 8854 8860 0.999323
147 8811 8817 0.999319
148 8865 8873 0.999098
149 8871 8883 0.998649
150 8609 8611 0.999768
151 8734 8743 0.998971
152 8870 8870 1
153 8698 8702 0.99954
154 8839 8847 0.999096
155 8708 8717 0.998968
156 8739 8742 0.999657
157 8720 8741 0.997598
158 8919 8936 0.998098
159 8698 8711 0.998508
160 8790 8793 0.999659
161 8747 8768 0.997605
162 8905 8914 0.99899
163 8815 8842 0.996946
164 8619 8641 0.997454
165 8689 8711 0.997474
166 8681 8715 0.996099
167 8685 8704 0.997817
168 8717 8728 0.99874
169 8768 8796 0.996817
170 8772 8781 0.998975
171 8759 8774 0.99829
172 8811 8834 0.997396
173 8859 8919 0.993273
174 8783 8789 0.999317
175 8845 8848 0.999661
176 8970 8973 0.999666
177 8775 8786 0.998748
178 8898 8921 0.997422
179 8946 8954 0.999107
180 8822 8832 0.998868
181 8828 8858 0.996613
182 8744 8771 0.996922
183 8777 8811 0.996141
184 8817 8828 0.998754
185 8646 8665 0.997807
186 9005 9022 0.998116
187 8720 8743 0.997369
188 8885 8901 0.998202
189 8744 8755 0.998744
190 8705 8729 0.997251
191 8691 8712 0.99759
192 8799 8802 0.999659
193 8749 8776 0.996923
194 8844 8868 0.997294
195 8868 8885 0.998087
196 8650 8663 0.998499
197 8765 8813 0.994554
198 8907 8919 0.998655
199 8631 8654 0.997342
200 8799 8804 0.999432
201 8859 8881 0.997523
202 8705 8768 0.992815
203 8788 8827 0.995582
204 8771 8778 0.999203
205 8745 8779 0.996127
206 8577 8610 0.996167
207 8756 8779 0.99738
208 8823 8849 0.997062
209 8680 8722 0.995185
210 8844 8857 0.998532
211 8754 8805 0.994208
212 8900 8949 0.994525
213 8765 8848 0.990619
214 8715 8805 0.989779
215 8774 8825 0.994221
216 8645 8654 0.99896
217 8805 8869 0.992784
218 8682 8785 0.988275
219 8649 8681 0.996314
220 8757 8830 0.991733
221 8855 8922 0.99249
222 8685 8718 0.996215
223 8661 8732 0.991869
224 8677 8736 0.993246
225 8800 8805 0.999432
226 8480 8500 0.997647
227 8606 8711 0.987946
228 8681 8700 0.997816
229 8696 8764 0.992241
230 8626 8699 0.991608
231 8720 8762 0.995207
232 8712 8766 0.99384
233 8519 8727 0.976166
234 8665 8699 0.996092
235 8772 8866 0.989398
236 8634 8729 0.989117
237 8770 8873 0.988392
238 8739 8783 0.99499
239 8692 8786 0.989301
240 8646 8673 0.996887
241 8649 8748 0.988683
242 8956 9027 0.992135
243 8725 8782 0.993509
244 8796 8825 0.996714
245 8842 8869 0.996956
246 8698 8719 0.997591
247 8787 8902 0.987082
248 8935 8966 0.996542
249 8610 8642 0.996297
250 8675 8684 0.998964
251 8826 8863 0.995825
252 8718 8730 0.998625
253 8801 8883 0.990769
254 8769 8836 0.992417
255 8846 8891 0.994939
256 8875 8904 0.996743
257 8556 8699 0.983561
258 8662 8720 0.993349
259 8771 8873 0.988504
260 8894 8942 0.994632
261 8560 8658 0.988681
262 8628 8783 0.982352
263 8707 8927 0.975356
264 8715 8758 0.99509
265 8803 8951 0.983466
266 8938 9055 0.987079
267 8730 8868 0.984438
268 8702 8812 0.987517
269 8695 8844 0.983152
270 8707 8746 0.995541
271 8632 8735 0.988208
272 9003 9052 0.994587
273 8670 8739 0.992104
274 8695 8779 0.990432
275 8881 8917 0.995963
276 8820 8835 0.998302
277 8506 8676 0.980406
278 8696 8812 0.986836
279 8788 8831 0.995131
280 8748 8772 0.997264
281 8627 8774 0.983246
282 8600 8685 0.990213
283 8704 8907 0.977209
284 8836 8907 0.992029
285 8707 8801 0.989319
286 8785 8855 0.992095
287 8575 8696 0.986086
288 8847 8875 0.996845
289 8608 8781 0.980298
290 8769 8810 0.995346
291 8636 8783 0.983263
292 8695 8748 0.993941
293 8655 8820 0.981293
294 8840 8853 0.998532
295 8721 8794 0.991699
296 8657 8682 0.99712
297 8794 8847 0.994009
298 8663 8760 0.988927
299 8821 8889 0.99235
300 8791 8802 0.99875
301 8504 8563 0.99311
302 8725 8849 0.985987
303 8777 8903 0.985847
304 8792 8828 0.995922
305 8794 8887 0.989535
306 8757 8777 0.997721
307 8720 8919 0.977688
308 8756 8802 0.994774
309 8604 8724 0.986245
310 8696 8750 0.993829
311 8581 8799 0.975224
312 8809 8853 0.99503
313 8760 8968 0.976806
314 8710 8896 0.979092
315 8726 8807 0.990803
316 8681 8833 0.982792
317 8748 8982 0.973948
318 8628 8790 0.98157
319 8480 8669 0.978198
320 8785 8851 0.992543
321 8714 8866 0.982856
322 8789 8903 0.987195
323 8665 8824 0.981981
324 8855 8872 0.998084
325 8740 8768 0.996807
326 8771 8888 0.986836
327 8559 8720 0.981537
328 8805 8901 0.989215
329 8694 8797 0.988291
330 8862 8961 0.988952
331 8527 8727 0.977083
332 8341 8525 0.978416
333 8674 8843 0.980889
334 8589 8808 0.975136
335 8575 8847 0.969255
336 8660 8710 0.994259
337 8580 8926 0.961237
338 8610 8835 0.974533
339 8509 8771 0.970129
340 8647 8778 0.985076
341 8574 8793 0.975094
342 8774 8848 0.991637
343 8765 8986 0.975406
344 8590 8690 0.988493
345 8567 8723 0.982116
346 8640 8876 0.973411
347 8471 8801 0.962504
348 8767 8826 0.993315
349 8635 8845 0.976258
350 8819 8845 0.99706
351 8674 8787 0.98714
352 8584 8629 0.994785
353 8479 8778 0.965938
354 8753 8838 0.990382
355 8725 8946 0.975296
356 8598 8742 0.983528
357 8698 8817 0.986503
358 8871 9056 0.979572
359 8596 8874 0.968673
360 8908 8958 0.994418
361 8351 8692 0.960769
362 8667 8943 0.969138
363 8582 8803 0.974895
364 8828 8887 0.993361
365 8551 8768 0.975251
366 8636 8802 0.981141
367 8176 8649 0.945312
368 8467 8613 0.983049
369 8590 8686 0.988948
370 8515 8663 0.982916
371 8714 8846 0.985078
372 8559 8641 0.99051
373 8558 8898 0.961789
374 8536 8712 0.979798
375 8529 8630 0.988297
376 8671 8741 0.991992
377 8623 8846 0.974791
378 8849 8901 0.994158
379 8373 8571 0.976899
380 8554 8723 0.980626
381 8636 8952 0.964701
382 8473 8851 0.957293
383 8490 8892 0.954791
384 8648 8692 0.994938
385 8610 8796 0.978854
386 8224 8667 0.948887
387 8649 8838 0.978615
388 8488 8751 0.969946
389 8368 8808 0.950045
390 8473 8582 0.987299
391 8421 8805 0.956388
392 8732 8813 0.990809
393 8588 8865 0.968754
394 8573 8893 0.964017
395 8657 8844 0.978856
396 8653 8685 0.996315
397 8725 8944 0.975514
398 8566 8791 0.974406
399 8624 8698 0.991492
400 8750 8773 0.997378
401 8540 8805 0.969903
402 8759 8884 0.98593
403 8447 8710 0.969805
404 8821 8976 0.982732
405 8700 8828 0.985501
406 8519 8636 0.986452
407 8448 8760 0.964384
408 8702 8772 0.99202
409 8210 8725 0.940974
410 8752 8889 0.984588
411 8272 8671 0.953985
412 8391 8673 0.967485
413 8567 8940 0.958277
414 8656 8944 0.9678
415 8347 8701 0.959315
416 8538 8744 0.976441
417 8355 8862 0.942789
418 8360 8760 0.954338
419 8255 8776 0.940634
420 8580 8662 0.990533
421 8403 8761 0.959137
422 8272 8782 0.941927
423 8555 8746 0.978161
424 8555 8651 0.988903
425 8581 8744 0.981359
426 8660 8800 0.984091
427 8445 8772 0.962722
428 8305 8752 0.948926
429 8464 8746 0.967757
430 8274 8588 0.963437
431 8025 8667 0.925926
432 8821 8875 0.993915
433 8019 8665 0.925447
434 8300 8714 0.95249
435 8478 8785 0.965054
436 8298 8779 0.94521
437 8175 8625 0.947826
438 8524 8746 0.974617
439 8455 8903 0.94968
440 8589 8731 0.983736
441 8514 8747 0.973362
442 8477 8770 0.966591
443 8400 8887 0.945201
444 8735 8868 0.985002
445 8453 8814 0.959042
446 8501 8807 0.965255
447 8551 8861 0.965015
448 8825 8901 0.991462
449 8212 8620 0.952668
450 8756 8788 0.996359
451 8488 8841 0.960072
452 8261 8573 0.963607
453 8434 8810 0.957321
454 8442 8769 0.96271
455 8677 8907 0.974178
456 8649 8712 0.992769
457 8101 8735 0.927418
458 8255 8699 0.94896
459 8460 8713 0.970963
460 8639 8850 0.976158
461 8194 8808 0.930291
462 8721 8835 0.987097
463 8223 8835 0.93073
464 8425 8821 0.955107
465 8483 8838 0.959833
466 7965 8725 0.912894
467 8373 8934 0.937206
468 8602 8688 0.990101
469 8243 8647 0.953279
470 8406 8719 0.964101
471 8439 8906 0.947563
472 8431 8768 0.961565
473 8367 8793 0.951552
474 8457 8714 0.970507
475 8663 8876 0.976003
476 8683 8791 0.987715
477 8480 8770 0.966933
478 8321 8864 0.938741
479 8361 8749 0.955652
480 8669 8779 0.98747
481 8417 8857 0.950322
482 8498 8946 0.949922
483 8545 8826 0.968162
484 8324 8647 0.962646
485 8394 8767 0.957454
486 8719 8949 0.974299
487 8221 8785 0.9358
488 8385 8667 0.967463
489 8234 8731 0.943076
490 8635 8771 0.984494
491 8134 8654 0.939912
492 8704 8798 0.989316
493 8292 8844 0.937585
494 8635 8923 0.967724
495 8443 8698 0.970683
496 8734 8866 0.985112
497 8565 8818 0.971309
498 8675 8842 0.981113
499 8359 8797 0.95021
500 8815 8882 0.992457
501 8478 8748 0.969136
502 8379 8731 0.959684
503 8416 8777 0.95887
504 8769 8802 0.996251
505 8295 8669 0.956858
506 8511 8758 0.971797
507 8355 8776 0.952028
508 8434 8786 0.959936
509 8190 8787 0.932059
510 8680 8851 0.98068
511 8366 8818 0.948741
512 8575 8879 0.965762
513 8348 8752 0.953839
514 8293 8884 0.933476
515 8438 8923 0.945646
516 8477 8795 0.963843
517 8325 8887 0.936762
518 8565 8970 0.954849
519 8237 8746 0.941802
520 8591 8816 0.974478
521 8262 8871 0.931349
522 8725 8991 0.970415
523 8311 8870 0.936979
524 8346 8775 0.951111
525 8595 8775 0.979487
526 8278 8835 0.936955
527 8117 8669 0.936325
528 8502 8607 0.987801
529 8330 8873 0.938803
530 8571 8985 0.953923
531 8378 8840 0.947738
532 8500 8831 0.962518
533 7868 8642 0.910437
534 8376 8925 0.938487
535 8157 8861 0.920551
536 8337 8837 0.94342
537 7943 8576 0.926189
538 8058 8852 0.910303
539 8510 8838 0.962888
540 8255 8550 0.965497
541 7892 8835 0.893265
542 8005 8830 0.906569
543 7917 8792 0.900478
544 8390 8752 0.958638
545 7963 8818 0.903039
546 8808 8972 0.981721
547 8110 8813 0.920231
548 8332 8869 0.939452
549 8442 8890 0.949606
550 8772 8871 0.98884
551 8215 8926 0.920345
552 8795 8944 0.983341
553 8435 8951 0.942353
554 8070 8862 0.91063
555 8241 8906 0.925331
556 8151 8859 0.920081
557 7730 8782 0.88021
558 8464 8810 0.960726
559 7933 8678 0.914151
560 8443 8732 0.966903
561 8359 8882 0.941117
562 7957 8751 0.909268
563 7761 8946 0.867539
564 8410 8773 0.958623
565 7954 8739 0.910173
566 7904 8882 0.88989
567 8264 8694 0.950541
568 8318 8769 0.948569
569 7974 8830 0.903058
570 8347 8703 0.959095
571 7990 8741 0.914083
572 8296 8744 0.948765
573 8245 8898 0.926613
574 8456 8697 0.972289
575 8541 8805 0.970017
576 8776 8856 0.990967
577 8176 8868 0.921967
578 8103 8865 0.914044
579 8181 8772 0.932627
580 8606 9022 0.95389
581 8261 8841 0.934397
582 8212 8772 0.936161
583 8030 8852 0.90714
584 8324 8689 0.957993
585 8461 8882 0.952601
586 7818 8666 0.902146
587 7819 8845 0.884002
588 8799 9023 0.975175
589 7846 8802 0.891388
590 8499 8874 0.957742
591 8236 8938 0.921459
592 8244 8680 0.94977
593 8062 8899 0.905944
594 8681 8886 0.97693
595 8320 8672 0.95941
596 8449 8882 0.95125
597 8219 8866 0.927025
598 8449 8834 0.956418
599 8178 8851 0.923963
600 8792 8819 0.996938
601 8044 8774 0.9168
602 8304 8615 0.9639
603 8426 8831 0.954139
604 8342 8851 0.942492
605 8314 8782 0.946709
606 8521 8976 0.949309
607 8006 8963 0.893228
608 8511 8950 0.95095
609 8379 8989 0.932139
610 8149 8664 0.940559
611 7985 8829 0.904406
612 8563 8750 0.978629
613 7745 8715 0.888698
614 7879 8913 0.88399
615 8245 8714 0.946179
616 8561 8863 0.965926
617 7819 8955 0.873143
618 8164 8737 0.934417
619 7734 8722 0.886723
620 8143 8644 0.942041
621 8287 8738 0.948386
622 7739 8549 0.905252
623 8293 8912 0.930543
624 8648 8745 0.988908
625 8462 8820 0.95941
626 8261 8846 0.933868
627 8082 8698 0.929179
628 8049 8601 0.935821
629 8333 8916 0.934612
630 8605 8810 0.976731
631 7665 8580 0.893357
632 8251 8747 0.943295
633 7947 8895 0.893423
634 7654 8650 0.884855
635 8153 8923 0.913706
636 8361 8938 0.935444
637 8034 8669 0.92675
638 7928 8750 0.906057
639 7928 8597 0.922182
640 8230 8737 0.941971
641 7684 8816 0.871597
642 8239 8965 0.919018
643 7531 8767 0.859017
644 8477 8981 0.943882
645 8033 8840 0.90871
646 7988 8775 0.910313
647 7797 8718 0.894357
648 8662 8762 0.988587
649 8116 8918 0.91007
650 8702 8868 0.981281
651 8383 9013 0.930101
652 8073 8709 0.926972
653 7769 8836 0.879244
654 7999 8656 0.924099
655 7744 8885 0.871581
656 8274 8786 0.941725
657 8169 8878 0.92014
658 8151 8679 0.939163
659 7219 8680 0.831682
660 8401 8826 0.951847
661 7337 8824 0.831482
662 7508 8808 0.852407
663 7925 8791 0.90149
664 7955 8724 0.911852
665 7979 8708 0.916284
666 8253 8833 0.934337
667 7565 8795 0.860148
668 7746 8720 0.888303
669 7608 8639 0.880657
670 8215 8769 0.936823
671 7982 8718 0.915577
672 8499 8686 0.978471
673 7961 8822 0.902403
674 7987 8831 0.904428
675 8563 8812 0.971743
676 8182 8679 0.942735
677 7753 8721 0.889004
678 7872 8728 0.901925
679 8152 8811 0.925207
680 8462 8852 0.955942
681 7688 8785 0.875128
682 7772 8717 0.891591
683 7286 8838 0.824395
684 8312 8858 0.938361
685 7663 8747 0.876072
686 8102 8756 0.925308
687 7537 8786 0.857842
688 8088 8769 0.92234
689 7544 8963 0.841682
690 8345 8776 0.950889
691 7114 8814 0.807125
692 7962 8838 0.900883
693 8580 8972 0.956309
694 7953 8820 0.901701
695 7696 8809 0.873652
696 8516 8863 0.960848
697 7777 8588 0.905566
698 8069 8847 0.912061
699 8174 8912 0.91719
700 8790 8906 0.986975
701 7956 8889 0.895039
702 8539 8763 0.974438
703 7838 8723 0.898544
704 8562 8909 0.961051
705 8237 8895 0.926026
706 7804 8830 0.883805
707 7730 8728 0.885655
708 8339 8913 0.9356
709 7486 8812 0.849523
710 8026 8767 0.915478
711 7707 8715 0.884337
712 7991 8809 0.90714
713 7385 8857 0.833804
714 8418 8823 0.954097
715 7752 8868 0.874154
716 7738 8706 0.888812
717 7433 8839 0.840932
718 7596 8752 0.867916
719 7893 8907 0.886157
720 8509 8686 0.979622
721 8141 8712 0.934458
722 7987 8901 0.897315
723 7977 8824 0.904012
724 8113 8796 0.922351
725 8173 8709 0.938454
726 8413 8701 0.9669
727 7944 8892 0.893387
728 8635 8931 0.966857
729 8267 8796 0.939859
730 8486 9003 0.942575
731 7455 8673 0.859564
732 8029 8809 0.911454
733 7268 8769 0.828829
734 7504 8775 0.855157
735 8188 8802 0.930243
736 7957 8704 0.914177
737 7405 8841 0.837575
738 7953 8710 0.913088
739 7013 8837 0.793595
740 8009 8738 0.916571
741 7702 8687 0.886612
742 8041 8783 0.915519
743 7130 8851 0.805559
744 8488 8824 0.961922
745 7634 8806 0.866909
746 7757 8815 0.879977
747 8102 8819 0.918698
748 8376 8953 0.935552
749 8076 8866 0.910896
750 8561 8763 0.976949
751 7719 8749 0.882272
752 8255 8701 0.948742
753 7757 8735 0.888037
754 7978 8690 0.918067
755 7719 8642 0.893196
756 8691 8872 0.979599
757 7526 8706 0.864461
758 7492 8676 0.863532
759 7750 8808 0.879882
760 8266 8777 0.94178
761 7262 8825 0.82289
762 7963 8905 0.894217
763 7508 8817 0.851537
764 7645 8816 0.867173
765 7947 8625 0.921391
766 7469 8837 0.845196
767 7204 8792 0.819381
768 8308 8752 0.949269
769 7224 8871 0.814339
770 8341 8736 0.954785
771 7509 8752 0.857975
772 7533 8821 0.853985
773 7407 8807 0.841036
774 8245 8689 0.948901
775 8185 8807 0.929374
776 8058 8770 0.918814
777 7812 8824 0.885313
778 7202 8862 0.812683
779 7290 8848 0.823915
780 8314 8743 0.950932
781 7482 8720 0.858028
782 7510 8764 0.856915
783 7584 8728 0.868928
784 8061 8653 0.931584
785 7220 8868 0.814163
786 7473 8728 0.85621
787 6726 8858 0.759314
788 7534 8981 0.838882
789 7258 8775 0.827123
790 7978 8791 0.907519
791 7523 8868 0.848331
792 8568 8886 0.964213
793 7570 8920 0.848655
794 7596 8915 0.852047
795 8033 8936 0.898948
796 7787 8898 0.87514
797 7597 8804 0.862903
798 8393 8883 0.944838
799 7659 8796 0.870737
800 8777 8900 0.98618
801 8135 8921 0.911893
802 7630 8713 0.875703
803 8084 8967 0.901528
804 8109 8856 0.91565
805 7622 8720 0.874083
806 7669 8815 0.869994
807 7251 8772 0.826607
808 7999 8833 0.905581
809 6845 8733 0.783809
810 8330 8661 0.961783
811 6805 8883 0.76607
812 8016 8899 0.900775
813 6912 8767 0.788411
814 7429 8707 0.853222
815 7092 8726 0.812744
816 8253 8746 0.943631
817 6923 8935 0.774818
818 6972 8814 0.791014
819 7760 8650 0.89711
820 7879 8904 0.884883
821 6938 8747 0.793186
822 7082 8681 0.815805
823 7187 8908 0.806803
824 7861 8723 0.901181
825 8356 8837 0.94557
826 7758 8655 0.89636
827 6948 8594 0.808471
828 8108 8792 0.922202
829 6958 8896 0.782149
830 7648 8844 0.864767
831 7103 8746 0.812143
832 8139 8947 0.90969
833 7635 8801 0.867515
834 7764 8878 0.874521
835 6996 8720 0.802294
836 7718 8953 0.862057
837 7640 8877 0.860651
838 7165 8908 0.804333
839 6613 8785 0.75276
840 8414 8811 0.954943
841 6925 8809 0.786128
842 7246 8817 0.821821
843 7307 8925 0.818711
844 7329 8893 0.824131
845 7277 8740 0.832609
846 8139 8859 0.918727
847 7850 8809 0.891134
848 8116 8904 0.9115
849 7409 8854 0.836797
850 8480 8842 0.959059
851 7153 8881 0.805427
852 7956 8644 0.920407
853 6868 8726 0.787073
854 7543 8753 0.861762
855 8119 8981 0.90402
856 7625 8923 0.854533
857 6533 8849 0.738276
858 7998 8863 0.902403
859 6930 8680 0.798387
860 7518 8793 0.854998
861 7271 8869 0.819822
862 6537 8909 0.733752
863 6509 8867 0.73407
864 8314 8891 0.935103
865 7020 8737 0.803479
866 6659 8664 0.768583
867 7363 8913 0.826097
868 7598 8808 0.862625
869 7011 8727 0.803369
870 8110 8869 0.914421
871 7396 8957 0.825723
872 7693 8976 0.857063
873 7756 8782 0.88317
874 7549 8674 0.870302
875 8177 8771 0.932277
876 8153 8791 0.927426
877 7208 8776 0.821331
878 6804 8734 0.779025
879 7401 8911 0.830547
880 8119 8853 0.91709
881 6897 8775 0.785983
882 8468 8913 0.950073
883 7075 8869 0.797722
884 7575 8854 0.855546
885 7659 8796 0.870737
886 6703 8751 0.76597
887 6779 9040 0.749889
888 7901 8755 0.902456
889 6892 8614 0.800093
890 7805 8871 0.879833
891 7742 8824 0.87738
892 7296 8756 0.833257
893 7155 8803 0.812791
894 7567 8713 0.868472
895 7368 8678 0.849044
896 8463 8913 0.949512
897 7900 8811 0.896607
898 7693 8913 0.863121
899 7717 8771 0.879831
900 8621 8716 0.989101
901 7777 8886 0.875197
902 8026 8906 0.90119
903 7847 8677 0.904345
904 7911 8773 0.901744
905 7431 8890 0.835883
906 7651 8769 0.872505
907 6913 8832 0.782722
908 7206 8769 0.821758
909 7394 8768 0.843294
910 7952 8831 0.900464
911 6504 8875 0.732845
912 8039 8747 0.919058
913 6572 8720 0.75367
914 6418 8798 0.729484
915 7123 8629 0.825472
916 6754 8795 0.767936
917 6884 8672 0.793819
918 8114 8761 0.92615
919 6510 8816 0.73843
920 8140 8915 0.913068
921 6848 8649 0.791768
922 6685 8778 0.761563
923 7333 8867 0.826999
924 8608 9093 0.946662
925 7854 8728 0.899863
926 6810 8797 0.774128
927 7672 8774 0.874402
928 7571 8842 0.856254
929 6912 8844 0.781547
930 7934 8754 0.906329
931 7295 8625 0.845797
932 7087 8862 0.799707
933 7018 8875 0.790761
934 7047 8843 0.796902
935 7524 8746 0.860279
936 8674 8963 0.967756
937 6889 8732 0.788937
938 7565 8618 0.877814
939 7242 8893 0.814348
940 8039 8914 0.90184
941 6861 8930 0.768309
942 7611 8823 0.862632
943 6879 8919 0.771275
944 7611 8799 0.864985
945 7981 8886 0.898154
946 7317 8805 0.831005
947 6717 8786 0.764512
948 7812 8712 0.896694
949 7318 8827 0.829047
950 8362 8840 0.945928
951 6844 8732 0.783784
952 8074 8789 0.918648
953 6793 8818 0.770356
954 7883 8785 0.897325
955 6586 8801 0.748324
956 6723 8803 0.763717
957 7093 8706 0.814725
958 6849 8747 0.783011
959 6671 8719 0.765111
960 8282 8905 0.930039
961 6152 8747 0.703327
962 7015 8757 0.801073
963 7079 8749 0.809121
964 6717 8765 0.766343
965 6596 8682 0.759733
966 7669 8875 0.864113
967 6255 8891 0.70352
968 7631 8829 0.864311
969 7112 8877 0.801172
970 7756 8969 0.864756
971 6648 8796 0.755798
972 8071 8839 0.913112
973 7247 8738 0.829366
974 7118 8975 0.793092
975 8162 8721 0.935902
976 7740 8869 0.872703
977 6650 8698 0.764544
978 7095 8933 0.794246
979 6909 8829 0.782535
980 8004 8762 0.91349
981 7184 8910 0.806285
982 6416 8555 0.749971
983 6458 8892 0.726271
984 8014 8952 0.895219
985 6540 8724 0.749656
986 6888 8748 0.78738
987 7287 8876 0.820978
988 7504 8761 0.856523
989 6396 8806 0.726323
990 8001 8656 0.92433
991 6592 8737 0.754492
992 7841 8917 0.879332
993 7013 8883 0.789486
994 7700 8745 0.880503
995 6846 8721 0.785002
996 7851 8741 0.898181
997 7010 8837 0.793256
998 7056 8630 0.817613
999 7595 8696 0.87339

The most successful 3 digit numbers are 100,101,102,108,112,114,121,125,140,145,152 which had a successful solve for combination of numbers I tried. The least successful were 961 and 967 down at around 70% success.

Extension

What if we are interested breaking down target numbers vs # of big numbers? Below is a plot of the success rate vs target number for each of the big numbers. Target vs Number of Big Numbers You can see that 0 big numbers really suffers as you go to higher target numbers, the minimum for this was 0 big numbers trying to hit 997, with only 35% of games being solvable. Conversely 2 big numbers holds up pretty well.

My rationale here is again, that you burn a lot of small numbers to get up to the 900 range, then don't have many left to fine tune your answer.

Repo Details

This code is really thrown together, you're on your own.

  • One.java: Solves one case, takes the numbers on the command line and prints out how to solve it
  • Countdown.java: Draws games randomly to get stats on the solvability rates. Used to generate the tables below
  • Solver.java: The actual solver for a single case
  • analyze.py: Used to run a bit of data analysis
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