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reformat example enumeration

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filifa 2025-04-19 15:43:27 -04:00
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notebooks/problem0031.ipynb
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@ -36,11 +36,11 @@
"Now we can jump to a more interesting question: if we have 1, 2, and 5 cent coins, how many ways can we make 7 cents? It's not too difficult to enumerate all six ways by hand:\n", "Now we can jump to a more interesting question: if we have 1, 2, and 5 cent coins, how many ways can we make 7 cents? It's not too difficult to enumerate all six ways by hand:\n",
"$$\\begin{align}\n", "$$\\begin{align}\n",
"5 + 2 \\\\\n", "5 + 2 \\\\\n",
"5 + (2 \\times 1) \\\\\n", "5 + 1 + 1 \\\\\n",
"(3 \\times 2) + 1 \\\\\n", "2 + 2 + 2 + 1 \\\\\n",
"(2 \\times 2) + (3 \\times 1) \\\\\n", "2 + 2 + 1 + 1 + 1 \\\\\n",
"2 + (5 \\times 1) \\\\\n", "2 + 1 + 1 + 1 + 1 + 1 \\\\\n",
"(7 \\times 1)\n", "1 + 1 + 1 + 1 + 1 + 1 + 1\n",
"\\end{align}$$\n", "\\end{align}$$\n",
"But we can also use the generating functions we came up with above to find the total. One way is to cut off each infinite series after the $x^7$ term, then multiply them all together." "But we can also use the generating functions we came up with above to find the total. One way is to cut off each infinite series after the $x^7$ term, then multiply them all together."
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