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@ -875,282 +875,282 @@
"source": [ "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", "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", "\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" "\n"
] ]
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 27, "execution_count": 31,
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
{ {
"data": { "data": {
"text/plain": [ "text/plain": [
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" {0, 1, 2, 3, 4, 5, 6, 7},\n", " 205: {0, 1, 2, 3, 4, 5, 6, 7},\n",
" {0, 2, 4, 6},\n", " 206: {0, 2, 4, 6},\n",
" {0, 1, 2, 3, 4, 5, 6, 7},\n", " 207: {0, 1, 2, 3, 4, 5, 6, 7},\n",
" {0, 1, 2, 3},\n", " 208: {0, 1, 2, 3},\n",
" {0, 1, 2, 3, 4, 5, 6, 7},\n", " 209: {0, 1, 2, 3, 4, 5, 6, 7},\n",
" {0, 2, 4, 6},\n", " 210: {0, 2, 4, 6},\n",
" {0, 1, 2, 3, 4, 5, 6, 7},\n", " 211: {0, 1, 2, 3, 4, 5, 6, 7},\n",
" {0, 1, 4, 5},\n", " 212: {0, 1, 4, 5},\n",
" {0, 1, 2, 3, 4, 5, 6, 7},\n", " 213: {0, 1, 2, 3, 4, 5, 6, 7},\n",
" {0, 2, 4, 6},\n", " 214: {0, 2, 4, 6},\n",
" {0, 1, 2, 3, 4, 5, 6, 7},\n", " 215: {0, 1, 2, 3, 4, 5, 6, 7},\n",
" {0, 1, 2, 4, 5, 6},\n", " 216: {0, 1, 2, 4, 5, 6},\n",
" {0, 1, 2, 3, 4, 5, 6, 7},\n", " 217: {0, 1, 2, 3, 4, 5, 6, 7},\n",
" {0, 2, 4, 6},\n", " 218: {0, 2, 4, 6},\n",
" {0, 1, 2, 3, 4, 5, 6, 7},\n", " 219: {0, 1, 2, 3, 4, 5, 6, 7},\n",
" {0, 1, 4, 5},\n", " 220: {0, 1, 4, 5},\n",
" {0, 1, 2, 3, 4, 5, 6, 7},\n", " 221: {0, 1, 2, 3, 4, 5, 6, 7},\n",
" {0, 2, 4, 6},\n", " 222: {0, 2, 4, 6},\n",
" {0, 1, 2, 3, 4, 5, 6, 7},\n", " 223: {0, 1, 2, 3, 4, 5, 6, 7},\n",
" {0, 1, 2, 3, 4, 6},\n", " 224: {0, 1, 2, 3, 4, 6},\n",
" {0, 1, 2, 3, 4, 5, 6, 7},\n", " 225: {0, 1, 2, 3, 4, 5, 6, 7},\n",
" {0, 2, 4, 6},\n", " 226: {0, 2, 4, 6},\n",
" {0, 1, 2, 3, 4, 5, 6, 7},\n", " 227: {0, 1, 2, 3, 4, 5, 6, 7},\n",
" {0, 1, 4, 5},\n", " 228: {0, 1, 4, 5},\n",
" {0, 1, 2, 3, 4, 5, 6, 7},\n", " 229: {0, 1, 2, 3, 4, 5, 6, 7},\n",
" {0, 2, 4, 6},\n", " 230: {0, 2, 4, 6},\n",
" {0, 1, 2, 3, 4, 5, 6, 7},\n", " 231: {0, 1, 2, 3, 4, 5, 6, 7},\n",
" {0, 1, 2, 4, 5, 6},\n", " 232: {0, 1, 2, 4, 5, 6},\n",
" {0, 1, 2, 3, 4, 5, 6, 7},\n", " 233: {0, 1, 2, 3, 4, 5, 6, 7},\n",
" {0, 2, 4, 6},\n", " 234: {0, 2, 4, 6},\n",
" {0, 1, 2, 3, 4, 5, 6, 7},\n", " 235: {0, 1, 2, 3, 4, 5, 6, 7},\n",
" {0, 1, 4, 5},\n", " 236: {0, 1, 4, 5},\n",
" {0, 1, 2, 3, 4, 5, 6, 7},\n", " 237: {0, 1, 2, 3, 4, 5, 6, 7},\n",
" {0, 2, 4, 6},\n", " 238: {0, 2, 4, 6},\n",
" {0, 1, 2, 3, 4, 5, 6, 7},\n", " 239: {0, 1, 2, 3, 4, 5, 6, 7},\n",
" {0, 1, 2, 3},\n", " 240: {0, 1, 2, 3},\n",
" {0, 1, 2, 3, 4, 5, 6, 7},\n", " 241: {0, 1, 2, 3, 4, 5, 6, 7},\n",
" {0, 2, 4, 6},\n", " 242: {0, 2, 4, 6},\n",
" {0, 1, 2, 3, 4, 5, 6, 7},\n", " 243: {0, 1, 2, 3, 4, 5, 6, 7},\n",
" {0, 1, 4, 5},\n", " 244: {0, 1, 4, 5},\n",
" {0, 1, 2, 3, 4, 5, 6, 7},\n", " 245: {0, 1, 2, 3, 4, 5, 6, 7},\n",
" {0, 2, 4, 6},\n", " 246: {0, 2, 4, 6},\n",
" {0, 1, 2, 3, 4, 5, 6, 7},\n", " 247: {0, 1, 2, 3, 4, 5, 6, 7},\n",
" {0, 1, 2, 4, 5, 6},\n", " 248: {0, 1, 2, 4, 5, 6},\n",
" {0, 1, 2, 3, 4, 5, 6, 7},\n", " 249: {0, 1, 2, 3, 4, 5, 6, 7},\n",
" {0, 2, 4, 6},\n", " 250: {0, 2, 4, 6},\n",
" {0, 1, 2, 3, 4, 5, 6, 7},\n", " 251: {0, 1, 2, 3, 4, 5, 6, 7},\n",
" {0, 1, 4, 5},\n", " 252: {0, 1, 4, 5},\n",
" {0, 1, 2, 3, 4, 5, 6, 7},\n", " 253: {0, 1, 2, 3, 4, 5, 6, 7},\n",
" {0, 2, 4, 6},\n", " 254: {0, 2, 4, 6},\n",
" {0, 1, 2, 3, 4, 5, 6, 7}]" " 255: {0, 1, 2, 3, 4, 5, 6, 7}}"
] ]
}, },
"execution_count": 27, "execution_count": 31,
"metadata": {}, "metadata": {},
"output_type": "execute_result" "output_type": "execute_result"
} }
], ],
"source": [ "source": [
"solution8" "dict(zip(range(1, 256), solution8))"
] ]
} }
], ],