How many ways are there to make change for $1.00?

Using US coins of 1¢, 5¢, 10¢, 25¢, 50¢, and $1, how many ways are there to make change for $1.00.  List all the ways.

\(\small{ \begin{array}{|r|r|r|r|r|r|r|r|} \hline Number & & 1~ \text{Cent} & 5~ \text{Cent} & 10~ \text{Cent} & 25~ \text{Cent} & 50~ \text{Cent} & $1\\ \hline 1. & 100 = &&&&&& 1\\ 2. & 100 = &&&&& 2\\ 3. & 100 = &&&& 2& 1\\ 4. & 100 = &&&& 4&\\ 5. & 100 = &&& 5&& 1\\ 6. & 100 = &&& 5& 2&\\ 7. & 100 = &&& 10&&\\ 8. & 100 = && 1& 2& 1& 1\\ 9. & 100 = && 1& 2& 3&\\ 10. & 100 = && 1& 7& 1&\\ 11. & 100 = && 2& 4&& 1\\ 12. & 100 = && 2& 4& 2&\\ 13. & 100 = && 2& 9&&\\ 14. & 100 = && 3& 1& 1& 1\\ 15. & 100 = && 3& 1& 3&\\ 16. & 100 = && 3& 6& 1&\\ 17. & 100 = && 4& 3&& 1\\ 18. & 100 = && 4& 3& 2&\\ 19. & 100 = && 4& 8&&\\ 20. & 100 = && 5&& 1& 1\\ 21. & 100 = && 5&& 3&\\ 22. & 100 = && 5& 5& 1&\\ 23. & 100 = && 6& 2&& 1\\ 24. & 100 = && 6& 2& 2&\\ 25. & 100 = && 6& 7&&\\ 26. & 100 = && 7& 4& 1&\\ 27. & 100 = && 8& 1&& 1\\ 28. & 100 = && 8& 1& 2&\\ 29. & 100 = && 8& 6&&\\ 30. & 100 = && 9& 3& 1&\\ 31. & 100 = && 10&&& 1\\ 32. & 100 = && 10&& 2&\\ 33. & 100 = && 10& 5&&\\ 34. & 100 = && 11& 2& 1&\\ 35. & 100 = && 12& 4&&\\ 36. & 100 = && 13& 1& 1&\\ 37. & 100 = && 14& 3&&\\ 38. & 100 = && 15&& 1&\\ 39. & 100 = && 16& 2&&\\ 40. & 100 = && 18& 1&&\\ 41. & 100 = && 20&&&\\ 42. & 100 = & 5&& 2& 1& 1\\ 43. & 100 = & 5&& 2& 3&\\ 44. & 100 = & 5&& 7& 1&\\ 45. & 100 = & 5& 1& 4&& 1\\ 46. & 100 = & 5& 1& 4& 2&\\ 47. & 100 = & 5& 1& 9&&\\ 48. & 100 = & 5& 2& 1& 1& 1\\ 49. & 100 = & 5& 2& 1& 3&\\ 50. & 100 = & 5& 2& 6& 1&\\ 51. & 100 = & 5& 3& 3&& 1\\ 52. & 100 = & 5& 3& 3& 2&\\ 53. & 100 = & 5& 3& 8&&\\ 54. & 100 = & 5& 4&& 1& 1\\ 55. & 100 = & 5& 4&& 3&\\ 56. & 100 = & 5& 4& 5& 1&\\ 57. & 100 = & 5& 5& 2&& 1\\ 58. & 100 = & 5& 5& 2& 2&\\ 59. & 100 = & 5& 5& 7&&\\ 60. & 100 = & 5& 6& 4& 1&\\ 61. & 100 = & 5& 7& 1&& 1\\ 62. & 100 = & 5& 7& 1& 2&\\ 63. & 100 = & 5& 7& 6&&\\ 64. & 100 = & 5& 8& 3& 1&\\ 65. & 100 = & 5& 9&&& 1\\ 66. & 100 = & 5& 9&& 2&\\ 67. & 100 = & 5& 9& 5&&\\ 68. & 100 = & 5& 10& 2& 1&\\ 69. & 100 = & 5& 11& 4&&\\ 70. & 100 = & 5& 12& 1& 1&\\ 71. & 100 = & 5& 13& 3&&\\ 72. & 100 = & 5& 14&& 1&\\ 73. & 100 = & 5& 15& 2&&\\ 74. & 100 = & 5& 17& 1&&\\ 75. & 100 = & 5& 19&&&\\ 76. & 100 = & 10&& 4&& 1\\ 77. & 100 = & 10&& 4& 2&\\ 78. & 100 = & 10&& 9&&\\ 79. & 100 = & 10& 1& 1& 1& 1\\ 80. & 100 = & 10& 1& 1& 3&\\ 81. & 100 = & 10& 1& 6& 1&\\ 82. & 100 = & 10& 2& 3&& 1\\ 83. & 100 = & 10& 2& 3& 2&\\ 84. & 100 = & 10& 2& 8&&\\ 85. & 100 = & 10& 3&& 1& 1\\ 86. & 100 = & 10& 3&& 3&\\ 87. & 100 = & 10& 3& 5& 1&\\ 88. & 100 = & 10& 4& 2&& 1\\ 89. & 100 = & 10& 4& 2& 2&\\ 90. & 100 = & 10& 4& 7&&\\ 91. & 100 = & 10& 5& 4& 1&\\ 92. & 100 = & 10& 6& 1&& 1\\ 93. & 100 = & 10& 6& 1& 2&\\ 94. & 100 = & 10& 6& 6&&\\ 95. & 100 = & 10& 7& 3& 1&\\ 96. & 100 = & 10& 8&&& 1\\ 97. & 100 = & 10& 8&& 2&\\ 98. & 100 = & 10& 8& 5&&\\ 99. & 100 = & 10& 9& 2& 1&\\ 100. & 100 = & 10& 10& 4&&\\ 101. & 100 = & 10& 11& 1& 1&\\ 102. & 100 = & 10& 12& 3&&\\ 103. & 100 = & 10& 13&& 1&\\ 104. & 100 = & 10& 14& 2&&\\ 105. & 100 = & 10& 16& 1&&\\ 106. & 100 = & 10& 18&&&\\ 107. & 100 = & 15&& 1& 1& 1\\ 108. & 100 = & 15&& 1& 3&\\ 109. & 100 = & 15&& 6& 1&\\ 110. & 100 = & 15& 1& 3&& 1\\ 111. & 100 = & 15& 1& 3& 2&\\ 112. & 100 = & 15& 1& 8&&\\ 113. & 100 = & 15& 2&& 1& 1\\ 114. & 100 = & 15& 2&& 3&\\ 115. & 100 = & 15& 2& 5& 1&\\ 116. & 100 = & 15& 3& 2&& 1\\ 117. & 100 = & 15& 3& 2& 2&\\ 118. & 100 = & 15& 3& 7&&\\ 119. & 100 = & 15& 4& 4& 1&\\ 120. & 100 = & 15& 5& 1&& 1\\ 121. & 100 = & 15& 5& 1& 2&\\ 122. & 100 = & 15& 5& 6&&\\ 123. & 100 = & 15& 6& 3& 1&\\ 124. & 100 = & 15& 7&&& 1\\ 125. & 100 = & 15& 7&& 2&\\ 126. & 100 = & 15& 7& 5&&\\ 127. & 100 = & 15& 8& 2& 1&\\ 128. & 100 = & 15& 9& 4&&\\ 129. & 100 = & 15& 10& 1& 1&\\ 130. & 100 = & 15& 11& 3&&\\ 131. & 100 = & 15& 12&& 1&\\ 132. & 100 = & 15& 13& 2&&\\ 133. & 100 = & 15& 15& 1&&\\ 134. & 100 = & 15& 17&&&\\ 135. & 100 = & 20&& 3&& 1\\ 136. & 100 = & 20&& 3& 2&\\ 137. & 100 = & 20&& 8&&\\ 138. & 100 = & 20& 1&& 1& 1\\ 139. & 100 = & 20& 1&& 3&\\ 140. & 100 = & 20& 1& 5& 1&\\ 141. & 100 = & 20& 2& 2&& 1\\ 142. & 100 = & 20& 2& 2& 2&\\ 143. & 100 = & 20& 2& 7&&\\ 144. & 100 = & 20& 3& 4& 1&\\ 145. & 100 = & 20& 4& 1&& 1\\ 146. & 100 = & 20& 4& 1& 2&\\ 147. & 100 = & 20& 4& 6&&\\ 148. & 100 = & 20& 5& 3& 1&\\ 149. & 100 = & 20& 6&&& 1\\ 150. & 100 = & 20& 6&& 2&\\ 151. & 100 = & 20& 6& 5&&\\ 152. & 100 = & 20& 7& 2& 1&\\ 153. & 100 = & 20& 8& 4&&\\ 154. & 100 = & 20& 9& 1& 1&\\ 155. & 100 = & 20& 10& 3&&\\ 156. & 100 = & 20& 11&& 1&\\ 157. & 100 = & 20& 12& 2&&\\ 158. & 100 = & 20& 14& 1&&\\ 159. & 100 = & 20& 16&&&\\ 160. & 100 = & 25&&& 1& 1\\ 161. & 100 = & 25&&& 3&\\ 162. & 100 = & 25&& 5& 1&\\ 163. & 100 = & 25& 1& 2&& 1\\ 164. & 100 = & 25& 1& 2& 2&\\ 165. & 100 = & 25& 1& 7&&\\ 166. & 100 = & 25& 2& 4& 1&\\ 167. & 100 = & 25& 3& 1&& 1\\ 168. & 100 = & 25& 3& 1& 2&\\ 169. & 100 = & 25& 3& 6&&\\ 170. & 100 = & 25& 4& 3& 1&\\ 171. & 100 = & 25& 5&&& 1\\ 172. & 100 = & 25& 5&& 2&\\ 173. & 100 = & 25& 5& 5&&\\ 174. & 100 = & 25& 6& 2& 1&\\ 175. & 100 = & 25& 7& 4&&\\ 176. & 100 = & 25& 8& 1& 1&\\ 177. & 100 = & 25& 9& 3&&\\ 178. & 100 = & 25& 10&& 1&\\ 179. & 100 = & 25& 11& 2&&\\ 180. & 100 = & 25& 13& 1&&\\ 181. & 100 = & 25& 15&&&\\ 182. & 100 = & 30&& 2&& 1\\ 183. & 100 = & 30&& 2& 2&\\ 184. & 100 = & 30&& 7&&\\ 185. & 100 = & 30& 1& 4& 1&\\ 186. & 100 = & 30& 2& 1&& 1\\ 187. & 100 = & 30& 2& 1& 2&\\ 188. & 100 = & 30& 2& 6&&\\ 189. & 100 = & 30& 3& 3& 1&\\ 190. & 100 = & 30& 4&&& 1\\ 191. & 100 = & 30& 4&& 2&\\ 192. & 100 = & 30& 4& 5&&\\ 193. & 100 = & 30& 5& 2& 1&\\ 194. & 100 = & 30& 6& 4&&\\ 195. & 100 = & 30& 7& 1& 1&\\ 196. & 100 = & 30& 8& 3&&\\ 197. & 100 = & 30& 9&& 1&\\ 198. & 100 = & 30& 10& 2&&\\ 199. & 100 = & 30& 12& 1&&\\ 200. & 100 = & 30& 14&&&\\ 201. & 100 = & 35&& 4& 1&\\ 202. & 100 = & 35& 1& 1&& 1\\ 203. & 100 = & 35& 1& 1& 2&\\ 204. & 100 = & 35& 1& 6&&\\ 205. & 100 = & 35& 2& 3& 1&\\ 206. & 100 = & 35& 3&&& 1\\ 207. & 100 = & 35& 3&& 2&\\ 208. & 100 = & 35& 3& 5&&\\ 209. & 100 = & 35& 4& 2& 1&\\ 210. & 100 = & 35& 5& 4&&\\ 211. & 100 = & 35& 6& 1& 1&\\ 212. & 100 = & 35& 7& 3&&\\ 213. & 100 = & 35& 8&& 1&\\ 214. & 100 = & 35& 9& 2&&\\ 215. & 100 = & 35& 11& 1&&\\ 216. & 100 = & 35& 13&&&\\ 217. & 100 = & 40&& 1&& 1\\ 218. & 100 = & 40&& 1& 2&\\ 219. & 100 = & 40&& 6&&\\ 220. & 100 = & 40& 1& 3& 1&\\ 221. & 100 = & 40& 2&&& 1\\ 222. & 100 = & 40& 2&& 2&\\ 223. & 100 = & 40& 2& 5&&\\ 224. & 100 = & 40& 3& 2& 1&\\ 225. & 100 = & 40& 4& 4&&\\ 226. & 100 = & 40& 5& 1& 1&\\ 227. & 100 = & 40& 6& 3&&\\ 228. & 100 = & 40& 7&& 1&\\ 229. & 100 = & 40& 8& 2&&\\ 230. & 100 = & 40& 10& 1&&\\ 231. & 100 = & 40& 12&&&\\ 232. & 100 = & 45&& 3& 1&\\ 233. & 100 = & 45& 1&&& 1\\ 234. & 100 = & 45& 1&& 2&\\ 235. & 100 = & 45& 1& 5&&\\ 236. & 100 = & 45& 2& 2& 1&\\ 237. & 100 = & 45& 3& 4&&\\ 238. & 100 = & 45& 4& 1& 1&\\ 239. & 100 = & 45& 5& 3&&\\ 240. & 100 = & 45& 6&& 1&\\ 241. & 100 = & 45& 7& 2&&\\ 242. & 100 = & 45& 9& 1&&\\ 243. & 100 = & 45& 11&&&\\ 244. & 100 = & 50&&&& 1\\ 245. & 100 = & 50&&& 2&\\ 246. & 100 = & 50&& 5&&\\ 247. & 100 = & 50& 1& 2& 1&\\ 248. & 100 = & 50& 2& 4&&\\ 249. & 100 = & 50& 3& 1& 1&\\ 250. & 100 = & 50& 4& 3&&\\ 251. & 100 = & 50& 5&& 1&\\ 252. & 100 = & 50& 6& 2&&\\ 253. & 100 = & 50& 8& 1&&\\ 254. & 100 = & 50& 10&&&\\ 255. & 100 = & 55&& 2& 1&\\ 256. & 100 = & 55& 1& 4&&\\ 257. & 100 = & 55& 2& 1& 1&\\ 258. & 100 = & 55& 3& 3&&\\ 259. & 100 = & 55& 4&& 1&\\ 260. & 100 = & 55& 5& 2&&\\ 261. & 100 = & 55& 7& 1&&\\ 262. & 100 = & 55& 9&&&\\ 263. & 100 = & 60&& 4&&\\ 264. & 100 = & 60& 1& 1& 1&\\ 265. & 100 = & 60& 2& 3&&\\ 266. & 100 = & 60& 3&& 1&\\ 267. & 100 = & 60& 4& 2&&\\ 268. & 100 = & 60& 6& 1&&\\ 269. & 100 = & 60& 8&&&\\ 270. & 100 = & 65&& 1& 1&\\ 271. & 100 = & 65& 1& 3&&\\ 272. & 100 = & 65& 2&& 1&\\ 273. & 100 = & 65& 3& 2&&\\ 274. & 100 = & 65& 5& 1&&\\ 275. & 100 = & 65& 7&&&\\ 276. & 100 = & 70&& 3&&\\ 277. & 100 = & 70& 1&& 1&\\ 278. & 100 = & 70& 2& 2&&\\ 279. & 100 = & 70& 4& 1&&\\ 280. & 100 = & 70& 6&&&\\ 281. & 100 = & 75&&& 1&\\ 282. & 100 = & 75& 1& 2&&\\ 283. & 100 = & 75& 3& 1&&\\ 284. & 100 = & 75& 5&&&\\ 285. & 100 = & 80&& 2&&\\ 286. & 100 = & 80& 2& 1&&\\ 287. & 100 = & 80& 4&&&\\ 288. & 100 = & 85& 1& 1&&\\ 289. & 100 = & 85& 3&&&\\ 290. & 100 = & 90&& 1&&\\ 291. & 100 = & 90& 2&&&\\ 292. & 100 = & 95& 1&&&\\ 293. & 100 = &100&&&&\\ \hline \end{array} } \)