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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",
"$$\\begin{align}\n",
"5 + 2 \\\\\n",
"5 + (2 \\times 1) \\\\\n",
"(3 \\times 2) + 1 \\\\\n",
"(2 \\times 2) + (3 \\times 1) \\\\\n",
"2 + (5 \\times 1) \\\\\n",
"(7 \\times 1)\n",
"5 + 1 + 1 \\\\\n",
"2 + 2 + 2 + 1 \\\\\n",
"2 + 2 + 1 + 1 + 1 \\\\\n",
"2 + 1 + 1 + 1 + 1 + 1 \\\\\n",
"1 + 1 + 1 + 1 + 1 + 1 + 1\n",
"\\end{align}$$\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."
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