From 4f401472129cbf1766e0168f757457028707520c Mon Sep 17 00:00:00 2001 From: filifa Date: Sat, 19 Apr 2025 15:43:27 -0400 Subject: [PATCH] reformat example enumeration --- notebooks/problem0031.ipynb | 10 +++++----- 1 file changed, 5 insertions(+), 5 deletions(-) diff --git a/notebooks/problem0031.ipynb b/notebooks/problem0031.ipynb index 12adb72..167f909 100644 --- a/notebooks/problem0031.ipynb +++ b/notebooks/problem0031.ipynb @@ -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." ]