293 Ways: Change for a Dollar

Did you know there are 293 different ways to make change for a dollar?

This is a fun (if somewhat time consuming) exercise for counting money. Have your students try to list all 293 coin combinations. The list below will come in handy when checking papers.

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

CONTRIBUTORS: Thanks to Cindy Stogsdill from Syracuse for contributing the list. Beth Dolezal’s class at Glover Middle School in Spokane, WA, contributed a correct answer for #293 that wasn’t listed originally! And a BIG thanks to Joshua Yohe, a music theory teacher at his own alma mater, Carnegie Mellon. Joshua was actually writing a computer program (for fun!) that would compute the list of 293 ways for him. To check his program, he found our page of answers, but then he emailed us 3 different mistakes! Thanks to everyone for their contributions.

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