Add files via upload
This commit is contained in:
Peter Norvig
GitHub
@@ -143,106 +143,106 @@
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"name": "stdout",
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"output_type": "stream",
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"text": [
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" 2 beads: 0 0\n",
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"60 beads: 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1\n",
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"20 beads: 0 2 2 4 6 0 6 6 2 8 0 8 8 6 4 0 4 4 8 2\n",
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"60 beads: 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3\n",
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"20 beads: 0 4 4 8 2 0 2 2 4 6 0 6 6 2 8 0 8 8 6 4\n",
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" 3 beads: 0 5 5\n",
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"20 beads: 0 6 6 2 8 0 8 8 6 4 0 4 4 8 2 0 2 2 4 6\n",
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"60 beads: 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7\n",
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"20 beads: 0 8 8 6 4 0 4 4 8 2 0 2 2 4 6 0 6 6 2 8\n",
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"60 beads: 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9\n",
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"60 beads: 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9\n",
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"60 beads: 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0\n",
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"60 beads: 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1\n",
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"12 beads: 1 3 4 7 1 8 9 7 6 3 9 2\n",
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||||
"60 beads: 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3\n",
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||||
"60 beads: 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4\n",
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"60 beads: 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5\n",
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"60 beads: 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6\n",
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"12 beads: 1 8 9 7 6 3 9 2 1 3 4 7\n",
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||||
"60 beads: 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8\n",
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"20 beads: 2 0 2 2 4 6 0 6 6 2 8 0 8 8 6 4 0 4 4 8\n",
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||||
"12 beads: 2 1 3 4 7 1 8 9 7 6 3 9\n",
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"20 beads: 2 2 4 6 0 6 6 2 8 0 8 8 6 4 0 4 4 8 2 0\n",
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"60 beads: 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1\n",
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"20 beads: 2 4 6 0 6 6 2 8 0 8 8 6 4 0 4 4 8 2 0 2\n",
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||||
"60 beads: 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3\n",
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" 4 beads: 2 6 8 4\n",
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"60 beads: 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5\n",
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"20 beads: 2 8 0 8 8 6 4 0 4 4 8 2 0 2 2 4 6 0 6 6\n",
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||||
"60 beads: 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7\n",
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"60 beads: 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7\n",
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"60 beads: 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8\n",
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"60 beads: 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9\n",
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"60 beads: 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0\n",
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"12 beads: 3 4 7 1 8 9 7 6 3 9 2 1\n",
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"60 beads: 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2\n",
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"60 beads: 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3\n",
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"60 beads: 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4\n",
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"60 beads: 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5\n",
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"12 beads: 3 9 2 1 3 4 7 1 8 9 7 6\n",
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"20 beads: 4 0 4 4 8 2 0 2 2 4 6 0 6 6 2 8 0 8 8 6\n",
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"60 beads: 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7\n",
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" 4 beads: 4 2 6 8\n",
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"60 beads: 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9\n",
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"20 beads: 4 4 8 2 0 2 2 4 6 0 6 6 2 8 0 8 8 6 4 0\n",
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"60 beads: 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1\n",
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"20 beads: 4 6 0 6 6 2 8 0 8 8 6 4 0 4 4 8 2 0 2 2\n",
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"12 beads: 4 7 1 8 9 7 6 3 9 2 1 3\n",
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"20 beads: 4 8 2 0 2 2 4 6 0 6 6 2 8 0 8 8 6 4 0 4\n",
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"60 beads: 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5\n",
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" 3 beads: 5 0 5\n",
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"60 beads: 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6\n",
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"60 beads: 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7\n",
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"60 beads: 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8\n",
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"60 beads: 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9\n",
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" 3 beads: 5 5 0\n",
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"60 beads: 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1\n",
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"60 beads: 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2\n",
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"60 beads: 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3\n",
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"60 beads: 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4\n",
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"20 beads: 6 0 6 6 2 8 0 8 8 6 4 0 4 4 8 2 0 2 2 4\n",
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"60 beads: 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5\n",
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"20 beads: 6 2 8 0 8 8 6 4 0 4 4 8 2 0 2 2 4 6 0 6\n",
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||||
"12 beads: 6 3 9 2 1 3 4 7 1 8 9 7\n",
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"20 beads: 6 4 0 4 4 8 2 0 2 2 4 6 0 6 6 2 8 0 8 8\n",
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"60 beads: 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9\n",
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"20 beads: 6 6 2 8 0 8 8 6 4 0 4 4 8 2 0 2 2 4 6 0\n",
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"60 beads: 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1\n",
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" 4 beads: 6 8 4 2\n",
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"60 beads: 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3\n",
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"60 beads: 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3\n",
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"12 beads: 7 1 8 9 7 6 3 9 2 1 3 4\n",
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"60 beads: 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5\n",
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"60 beads: 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6\n",
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"60 beads: 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7\n",
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"60 beads: 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8\n",
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"12 beads: 7 6 3 9 2 1 3 4 7 1 8 9\n",
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"60 beads: 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0\n",
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"60 beads: 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1\n",
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"60 beads: 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2\n",
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"20 beads: 8 0 8 8 6 4 0 4 4 8 2 0 2 2 4 6 0 6 6 2\n",
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"60 beads: 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3\n",
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"20 beads: 8 2 0 2 2 4 6 0 6 6 2 8 0 8 8 6 4 0 4 4\n",
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"60 beads: 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5\n",
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" 4 beads: 8 4 2 6\n",
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"60 beads: 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7\n",
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"20 beads: 8 6 4 0 4 4 8 2 0 2 2 4 6 0 6 6 2 8 0 8\n",
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"60 beads: 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9\n",
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"20 beads: 8 8 6 4 0 4 4 8 2 0 2 2 4 6 0 6 6 2 8 0\n",
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"12 beads: 8 9 7 6 3 9 2 1 3 4 7 1\n",
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"60 beads: 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1\n",
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"60 beads: 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2\n",
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"12 beads: 9 2 1 3 4 7 1 8 9 7 6 3\n",
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"60 beads: 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4\n",
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"60 beads: 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5\n",
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"60 beads: 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6\n",
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"60 beads: 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7\n",
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"12 beads: 9 7 6 3 9 2 1 3 4 7 1 8\n",
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"60 beads: 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9\n",
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"60 beads: 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0\n"
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" 2 beads: 00\n",
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"60 beads: 011235831459437077415617853819099875279651673033695493257291\n",
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"20 beads: 02246066280886404482\n",
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"60 beads: 033695493257291011235831459437077415617853819099875279651673\n",
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"20 beads: 04482022460662808864\n",
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" 3 beads: 055\n",
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"20 beads: 06628088640448202246\n",
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"60 beads: 077415617853819099875279651673033695493257291011235831459437\n",
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"20 beads: 08864044820224606628\n",
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"60 beads: 099875279651673033695493257291011235831459437077415617853819\n",
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"60 beads: 101123583145943707741561785381909987527965167303369549325729\n",
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"60 beads: 112358314594370774156178538190998752796516730336954932572910\n",
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"60 beads: 123583145943707741561785381909987527965167303369549325729101\n",
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"12 beads: 134718976392\n",
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"60 beads: 145943707741561785381909987527965167303369549325729101123583\n",
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||||
"60 beads: 156178538190998752796516730336954932572910112358314594370774\n",
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"60 beads: 167303369549325729101123583145943707741561785381909987527965\n",
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||||
"60 beads: 178538190998752796516730336954932572910112358314594370774156\n",
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"12 beads: 189763921347\n",
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||||
"60 beads: 190998752796516730336954932572910112358314594370774156178538\n",
|
||||
"20 beads: 20224606628088640448\n",
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||||
"12 beads: 213471897639\n",
|
||||
"20 beads: 22460662808864044820\n",
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||||
"60 beads: 235831459437077415617853819099875279651673033695493257291011\n",
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||||
"20 beads: 24606628088640448202\n",
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"60 beads: 257291011235831459437077415617853819099875279651673033695493\n",
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" 4 beads: 2684\n",
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"60 beads: 279651673033695493257291011235831459437077415617853819099875\n",
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||||
"20 beads: 28088640448202246066\n",
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"60 beads: 291011235831459437077415617853819099875279651673033695493257\n",
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"60 beads: 303369549325729101123583145943707741561785381909987527965167\n",
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"60 beads: 314594370774156178538190998752796516730336954932572910112358\n",
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"60 beads: 325729101123583145943707741561785381909987527965167303369549\n",
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||||
"60 beads: 336954932572910112358314594370774156178538190998752796516730\n",
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"12 beads: 347189763921\n",
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"60 beads: 358314594370774156178538190998752796516730336954932572910112\n",
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"60 beads: 369549325729101123583145943707741561785381909987527965167303\n",
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"60 beads: 370774156178538190998752796516730336954932572910112358314594\n",
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||||
"60 beads: 381909987527965167303369549325729101123583145943707741561785\n",
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||||
"12 beads: 392134718976\n",
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||||
"20 beads: 40448202246066280886\n",
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"60 beads: 415617853819099875279651673033695493257291011235831459437077\n",
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" 4 beads: 4268\n",
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"60 beads: 437077415617853819099875279651673033695493257291011235831459\n",
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"20 beads: 44820224606628088640\n",
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"60 beads: 459437077415617853819099875279651673033695493257291011235831\n",
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"20 beads: 46066280886404482022\n",
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"12 beads: 471897639213\n",
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"20 beads: 48202246066280886404\n",
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"60 beads: 493257291011235831459437077415617853819099875279651673033695\n",
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" 3 beads: 505\n",
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"60 beads: 516730336954932572910112358314594370774156178538190998752796\n",
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"60 beads: 527965167303369549325729101123583145943707741561785381909987\n",
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"60 beads: 538190998752796516730336954932572910112358314594370774156178\n",
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"60 beads: 549325729101123583145943707741561785381909987527965167303369\n",
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" 3 beads: 550\n",
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||||
"60 beads: 561785381909987527965167303369549325729101123583145943707741\n",
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"60 beads: 572910112358314594370774156178538190998752796516730336954932\n",
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"60 beads: 583145943707741561785381909987527965167303369549325729101123\n",
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||||
"60 beads: 594370774156178538190998752796516730336954932572910112358314\n",
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"20 beads: 60662808864044820224\n",
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||||
"60 beads: 617853819099875279651673033695493257291011235831459437077415\n",
|
||||
"20 beads: 62808864044820224606\n",
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||||
"12 beads: 639213471897\n",
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"20 beads: 64044820224606628088\n",
|
||||
"60 beads: 651673033695493257291011235831459437077415617853819099875279\n",
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||||
"20 beads: 66280886404482022460\n",
|
||||
"60 beads: 673033695493257291011235831459437077415617853819099875279651\n",
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" 4 beads: 6842\n",
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||||
"60 beads: 695493257291011235831459437077415617853819099875279651673033\n",
|
||||
"60 beads: 707741561785381909987527965167303369549325729101123583145943\n",
|
||||
"12 beads: 718976392134\n",
|
||||
"60 beads: 729101123583145943707741561785381909987527965167303369549325\n",
|
||||
"60 beads: 730336954932572910112358314594370774156178538190998752796516\n",
|
||||
"60 beads: 741561785381909987527965167303369549325729101123583145943707\n",
|
||||
"60 beads: 752796516730336954932572910112358314594370774156178538190998\n",
|
||||
"12 beads: 763921347189\n",
|
||||
"60 beads: 774156178538190998752796516730336954932572910112358314594370\n",
|
||||
"60 beads: 785381909987527965167303369549325729101123583145943707741561\n",
|
||||
"60 beads: 796516730336954932572910112358314594370774156178538190998752\n",
|
||||
"20 beads: 80886404482022460662\n",
|
||||
"60 beads: 819099875279651673033695493257291011235831459437077415617853\n",
|
||||
"20 beads: 82022460662808864044\n",
|
||||
"60 beads: 831459437077415617853819099875279651673033695493257291011235\n",
|
||||
" 4 beads: 8426\n",
|
||||
"60 beads: 853819099875279651673033695493257291011235831459437077415617\n",
|
||||
"20 beads: 86404482022460662808\n",
|
||||
"60 beads: 875279651673033695493257291011235831459437077415617853819099\n",
|
||||
"20 beads: 88640448202246066280\n",
|
||||
"12 beads: 897639213471\n",
|
||||
"60 beads: 909987527965167303369549325729101123583145943707741561785381\n",
|
||||
"60 beads: 910112358314594370774156178538190998752796516730336954932572\n",
|
||||
"12 beads: 921347189763\n",
|
||||
"60 beads: 932572910112358314594370774156178538190998752796516730336954\n",
|
||||
"60 beads: 943707741561785381909987527965167303369549325729101123583145\n",
|
||||
"60 beads: 954932572910112358314594370774156178538190998752796516730336\n",
|
||||
"60 beads: 965167303369549325729101123583145943707741561785381909987527\n",
|
||||
"12 beads: 976392134718\n",
|
||||
"60 beads: 987527965167303369549325729101123583145943707741561785381909\n",
|
||||
"60 beads: 998752796516730336954932572910112358314594370774156178538190\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
@@ -252,7 +252,7 @@
|
||||
"def show(bracelets):\n",
|
||||
" \"\"\"Print each of the bracelets, preceeded by its number of beads.\"\"\"\n",
|
||||
" for beads in bracelets:\n",
|
||||
" print(f'{len(beads):2} beads:', *beads)\n",
|
||||
" print(f'{len(beads):2} beads:', ''.join(map(str, beads)))\n",
|
||||
"\n",
|
||||
"all_bracelets = [bracelet((first, second)) for first in digits for second in digits]\n",
|
||||
"\n",
|
||||
@@ -266,31 +266,29 @@
|
||||
"source": [
|
||||
"# How Many Bracelets?\n",
|
||||
"\n",
|
||||
"I showed 100 bracelets, because there are 100 two-digit starting pairs. But consider thesde three results:\n",
|
||||
"- 0 5 5\n",
|
||||
"- 5 0 5\n",
|
||||
"- 5 5 0\n",
|
||||
"I showed 100 bracelets, because there are 100 two-digit starting pairs. But consider these three results:\n",
|
||||
"- 055\n",
|
||||
"- 505\n",
|
||||
"- 550\n",
|
||||
"\n",
|
||||
"These are all different as *sequences*, but they are all the same as *circular bracelets*: two 5s and a 0. So let's see how many different bracelets there are. I'll do that by converting all three of these into one common form. I'll arbitrarily choose the form that would be the lowest number: 055 is lower than 505 or 550. Then I'll make a set of all the distinct common forms and show them:"
|
||||
"These are all different as *sequences*, but they are all the same as *circular bracelets*: if you start at the 0 and go around the circle they all are equal to \"055.\" So let's see how many *different* bracelets there are. I'll do that by converting all bracelets into one common form. Out of all the possible starting points on the circle, I'll arbitrarily choose the starting point that would yield the lowest number: 055 is lower than 505 or 550, so 055 will be the common form. Then I'll make a set of all the distinct common forms and show them:"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 6,
|
||||
"id": "9c6ed448-87a2-42f4-ab7b-75758e734cd2",
|
||||
"id": "9d1b4cca-cc8c-4268-9c5b-b9d2f2909948",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
" 2 beads: 0 0\n",
|
||||
" 4 beads: 2 6 8 4\n",
|
||||
" 3 beads: 0 5 5\n",
|
||||
"12 beads: 1 3 4 7 1 8 9 7 6 3 9 2\n",
|
||||
"60 beads: 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1\n",
|
||||
"20 beads: 0 2 2 4 6 0 6 6 2 8 0 8 8 6 4 0 4 4 8 2\n"
|
||||
]
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"(0, 5, 5)"
|
||||
]
|
||||
},
|
||||
"execution_count": 6,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
@@ -302,6 +300,29 @@
|
||||
" \"\"\"All possible rotations of bracelet.\"\"\"\n",
|
||||
" return [bracelet[i:] + bracelet[:i] for i in range(len(bracelet))]\n",
|
||||
"\n",
|
||||
"common_form((5, 0, 5))"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 7,
|
||||
"id": "9ae033fd-062e-4953-9603-4f82da516057",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
" 2 beads: 00\n",
|
||||
" 4 beads: 2684\n",
|
||||
" 3 beads: 055\n",
|
||||
"12 beads: 134718976392\n",
|
||||
"60 beads: 011235831459437077415617853819099875279651673033695493257291\n",
|
||||
"20 beads: 02246066280886404482\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"show({common_form(beads) for beads in all_bracelets})"
|
||||
]
|
||||
},
|
||||
|
||||
Reference in New Issue
Block a user