diff --git a/ipynb/Coin Flip.ipynb b/ipynb/Coin Flip.ipynb index 5f4ec79..2d34181 100644 --- a/ipynb/Coin Flip.ipynb +++ b/ipynb/Coin Flip.ipynb @@ -875,282 +875,282 @@ "source": [ "We can see that every odd-numbered move flips all four coins to eliminate the possibility of `TTTT`, flipping it to `HHHH`. We can also see that moves 2, 4, and 6 flip two coins and have the effect of eventually eliminating the two \"two heads\" sequences from the belief state, and then move 8 eliminates the \"three heads\" and \"one heads\" sequences, while bringing back the \"two heads\" possibilities. Repeating moves 2, 4, and 6 in moves 10, 12, and 14 then re-eliminates the \"two heads\", and move 15 gets the belief state down to `{'HHHH'}`.\n", "\n", - "You could call `show(solution8)`, but the results look bad unless you have a very wide (340 characters) screen to view it on. So I'll just show `solution8` itself:\n", + "You could call `show(solution8)`, but the results look bad unless you have a very wide (340 characters) screen to view it on. So I'll just show `solution8` itself, with move numbers:\n", "\n" ] }, { "cell_type": "code", - "execution_count": 27, + "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "[{0, 1, 2, 3, 4, 5, 6, 7},\n", - " {0, 2, 4, 6},\n", - " {0, 1, 2, 3, 4, 5, 6, 7},\n", - " {0, 1, 4, 5},\n", - " {0, 1, 2, 3, 4, 5, 6, 7},\n", - " {0, 2, 4, 6},\n", - " {0, 1, 2, 3, 4, 5, 6, 7},\n", - " {0, 1, 2, 4, 5, 6},\n", - " {0, 1, 2, 3, 4, 5, 6, 7},\n", - " {0, 2, 4, 6},\n", - " {0, 1, 2, 3, 4, 5, 6, 7},\n", - " {0, 1, 4, 5},\n", - " {0, 1, 2, 3, 4, 5, 6, 7},\n", - " {0, 2, 4, 6},\n", - " {0, 1, 2, 3, 4, 5, 6, 7},\n", - " {0, 1, 2, 3},\n", - " {0, 1, 2, 3, 4, 5, 6, 7},\n", - " {0, 2, 4, 6},\n", - " {0, 1, 2, 3, 4, 5, 6, 7},\n", - " {0, 1, 4, 5},\n", - " {0, 1, 2, 3, 4, 5, 6, 7},\n", - " {0, 2, 4, 6},\n", - " {0, 1, 2, 3, 4, 5, 6, 7},\n", - " {0, 1, 2, 4, 5, 6},\n", - " {0, 1, 2, 3, 4, 5, 6, 7},\n", - " {0, 2, 4, 6},\n", - " {0, 1, 2, 3, 4, 5, 6, 7},\n", - " {0, 1, 4, 5},\n", - " 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6},\n", - " {0, 1, 2, 3, 4, 5, 6, 7},\n", - " {0, 2, 4, 6},\n", - " {0, 1, 2, 3, 4, 5, 6, 7},\n", - " {0, 1, 4, 5},\n", - " {0, 1, 2, 3, 4, 5, 6, 7},\n", - " {0, 2, 4, 6},\n", - " {0, 1, 2, 3, 4, 5, 6, 7},\n", - " {0, 1, 2, 3},\n", - " {0, 1, 2, 3, 4, 5, 6, 7},\n", - " {0, 2, 4, 6},\n", - " {0, 1, 2, 3, 4, 5, 6, 7},\n", - " {0, 1, 4, 5},\n", - " {0, 1, 2, 3, 4, 5, 6, 7},\n", - " {0, 2, 4, 6},\n", - " {0, 1, 2, 3, 4, 5, 6, 7},\n", - " {0, 1, 2, 4, 5, 6},\n", - " {0, 1, 2, 3, 4, 5, 6, 7},\n", - " {0, 2, 4, 6},\n", - " {0, 1, 2, 3, 4, 5, 6, 7},\n", - " {0, 1, 4, 5},\n", - " {0, 1, 2, 3, 4, 5, 6, 7},\n", - " {0, 2, 4, 6},\n", - " {0, 1, 2, 3, 4, 5, 6, 7},\n", - " {0, 1, 2, 3, 4, 5},\n", - " {0, 1, 2, 3, 4, 5, 6, 7},\n", - " {0, 2, 4, 6},\n", - " {0, 1, 2, 3, 4, 5, 6, 7},\n", - " {0, 1, 4, 5},\n", - " {0, 1, 2, 3, 4, 5, 6, 7},\n", - " {0, 2, 4, 6},\n", - " {0, 1, 2, 3, 4, 5, 6, 7},\n", - " {0, 1, 2, 4, 5, 6},\n", - " {0, 1, 2, 3, 4, 5, 6, 7},\n", - " {0, 2, 4, 6},\n", - " {0, 1, 2, 3, 4, 5, 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6},\n", - " {0, 1, 2, 3, 4, 5, 6, 7},\n", - " {0, 1, 2, 3},\n", - " {0, 1, 2, 3, 4, 5, 6, 7},\n", - " {0, 2, 4, 6},\n", - " {0, 1, 2, 3, 4, 5, 6, 7},\n", - " {0, 1, 4, 5},\n", - " {0, 1, 2, 3, 4, 5, 6, 7},\n", - " {0, 2, 4, 6},\n", - " {0, 1, 2, 3, 4, 5, 6, 7},\n", - " {0, 1, 2, 4, 5, 6},\n", - " {0, 1, 2, 3, 4, 5, 6, 7},\n", - " {0, 2, 4, 6},\n", - " {0, 1, 2, 3, 4, 5, 6, 7},\n", - " {0, 1, 4, 5},\n", - " {0, 1, 2, 3, 4, 5, 6, 7},\n", - " {0, 2, 4, 6},\n", - " {0, 1, 2, 3, 4, 5, 6, 7}]" + "{1: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 2: {0, 2, 4, 6},\n", + " 3: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 4: {0, 1, 4, 5},\n", + " 5: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 6: {0, 2, 4, 6},\n", + " 7: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 8: {0, 1, 2, 4, 5, 6},\n", + " 9: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 10: {0, 2, 4, 6},\n", + " 11: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 12: {0, 1, 4, 5},\n", + " 13: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 14: {0, 2, 4, 6},\n", + " 15: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 16: {0, 1, 2, 3},\n", + " 17: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 18: {0, 2, 4, 6},\n", + " 19: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 20: {0, 1, 4, 5},\n", + " 21: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 22: {0, 2, 4, 6},\n", + " 23: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 24: {0, 1, 2, 4, 5, 6},\n", + " 25: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 26: {0, 2, 4, 6},\n", + " 27: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 28: {0, 1, 4, 5},\n", + " 29: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 30: {0, 2, 4, 6},\n", + " 31: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 32: {0, 1, 2, 3, 4, 6},\n", + " 33: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 34: {0, 2, 4, 6},\n", + " 35: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 36: {0, 1, 4, 5},\n", + " 37: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 38: {0, 2, 4, 6},\n", + " 39: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 40: {0, 1, 2, 4, 5, 6},\n", + " 41: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 42: {0, 2, 4, 6},\n", + " 43: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 44: {0, 1, 4, 5},\n", + " 45: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 46: {0, 2, 4, 6},\n", + " 47: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 48: {0, 1, 2, 3},\n", + " 49: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 50: {0, 2, 4, 6},\n", + " 51: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 52: {0, 1, 4, 5},\n", + " 53: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 54: {0, 2, 4, 6},\n", + " 55: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 56: {0, 1, 2, 4, 5, 6},\n", + " 57: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 58: {0, 2, 4, 6},\n", + " 59: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 60: {0, 1, 4, 5},\n", + " 61: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 62: {0, 2, 4, 6},\n", + " 63: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 64: {0, 1, 2, 3, 4, 5},\n", + " 65: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 66: {0, 2, 4, 6},\n", + " 67: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 68: {0, 1, 4, 5},\n", + " 69: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 70: {0, 2, 4, 6},\n", + " 71: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 72: {0, 1, 2, 4, 5, 6},\n", + " 73: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 74: {0, 2, 4, 6},\n", + " 75: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 76: {0, 1, 4, 5},\n", + " 77: {0, 1, 2, 3, 4, 5, 6, 7},\n", 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1, 4, 5},\n", + " 109: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 110: {0, 2, 4, 6},\n", + " 111: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 112: {0, 1, 2, 3},\n", + " 113: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 114: {0, 2, 4, 6},\n", + " 115: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 116: {0, 1, 4, 5},\n", + " 117: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 118: {0, 2, 4, 6},\n", + " 119: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 120: {0, 1, 2, 4, 5, 6},\n", + " 121: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 122: {0, 2, 4, 6},\n", + " 123: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 124: {0, 1, 4, 5},\n", + " 125: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 126: {0, 2, 4, 6},\n", + " 127: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 128: {0, 1, 2, 3, 4, 5, 6},\n", + " 129: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 130: {0, 2, 4, 6},\n", + " 131: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 132: {0, 1, 4, 5},\n", + " 133: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 134: {0, 2, 4, 6},\n", + " 135: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 136: {0, 1, 2, 4, 5, 6},\n", + " 137: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 138: {0, 2, 4, 6},\n", + " 139: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 140: {0, 1, 4, 5},\n", + " 141: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 142: {0, 2, 4, 6},\n", + " 143: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 144: {0, 1, 2, 3},\n", + " 145: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 146: {0, 2, 4, 6},\n", + " 147: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 148: {0, 1, 4, 5},\n", + " 149: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 150: {0, 2, 4, 6},\n", + " 151: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 152: {0, 1, 2, 4, 5, 6},\n", + " 153: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 154: {0, 2, 4, 6},\n", + " 155: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 156: {0, 1, 4, 5},\n", + " 157: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 158: {0, 2, 4, 6},\n", + " 159: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 160: {0, 1, 2, 3, 4, 6},\n", + " 161: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 162: {0, 2, 4, 6},\n", + " 163: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 164: {0, 1, 4, 5},\n", + " 165: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 166: {0, 2, 4, 6},\n", + " 167: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 168: {0, 1, 2, 4, 5, 6},\n", + " 169: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 170: {0, 2, 4, 6},\n", + " 171: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 172: {0, 1, 4, 5},\n", + " 173: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 174: {0, 2, 4, 6},\n", + " 175: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 176: {0, 1, 2, 3},\n", + " 177: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 178: {0, 2, 4, 6},\n", + " 179: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 180: {0, 1, 4, 5},\n", + " 181: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 182: {0, 2, 4, 6},\n", + " 183: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 184: {0, 1, 2, 4, 5, 6},\n", + " 185: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 186: {0, 2, 4, 6},\n", + " 187: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 188: {0, 1, 4, 5},\n", + " 189: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 190: {0, 2, 4, 6},\n", + " 191: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 192: {0, 1, 2, 3, 4, 5},\n", + " 193: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 194: {0, 2, 4, 6},\n", + " 195: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 196: {0, 1, 4, 5},\n", + " 197: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 198: {0, 2, 4, 6},\n", + " 199: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 200: {0, 1, 2, 4, 5, 6},\n", + " 201: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 202: {0, 2, 4, 6},\n", + " 203: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 204: {0, 1, 4, 5},\n", + " 205: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 206: {0, 2, 4, 6},\n", + " 207: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 208: {0, 1, 2, 3},\n", + " 209: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 210: {0, 2, 4, 6},\n", + " 211: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 212: {0, 1, 4, 5},\n", + " 213: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 214: {0, 2, 4, 6},\n", + " 215: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 216: {0, 1, 2, 4, 5, 6},\n", + " 217: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 218: {0, 2, 4, 6},\n", + " 219: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 220: {0, 1, 4, 5},\n", + " 221: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 222: {0, 2, 4, 6},\n", + " 223: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 224: {0, 1, 2, 3, 4, 6},\n", + " 225: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 226: {0, 2, 4, 6},\n", + " 227: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 228: {0, 1, 4, 5},\n", + " 229: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 230: {0, 2, 4, 6},\n", + " 231: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 232: {0, 1, 2, 4, 5, 6},\n", + " 233: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 234: {0, 2, 4, 6},\n", + " 235: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 236: {0, 1, 4, 5},\n", + " 237: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 238: {0, 2, 4, 6},\n", + " 239: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 240: {0, 1, 2, 3},\n", + " 241: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 242: {0, 2, 4, 6},\n", + " 243: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 244: {0, 1, 4, 5},\n", + " 245: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 246: {0, 2, 4, 6},\n", + " 247: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 248: {0, 1, 2, 4, 5, 6},\n", + " 249: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 250: {0, 2, 4, 6},\n", + " 251: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 252: {0, 1, 4, 5},\n", + " 253: {0, 1, 2, 3, 4, 5, 6, 7},\n", + " 254: {0, 2, 4, 6},\n", + " 255: {0, 1, 2, 3, 4, 5, 6, 7}}" ] }, - "execution_count": 27, + "execution_count": 31, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "solution8" + "dict(zip(range(1, 256), solution8))" ] } ],