How many different ways can you make 15 cents in change?

Answer 1

9 ways:

20 pennies

1 nickel 15 pennies

2 nickles 10 pennies

3 nickels 5 pennies

4 nickels

1 dime 10 pennies

1 dime 1 nickel 5 pennies

1 dime 2 nickels

2 dimes.

Answer 2

13 ways - 5 pennies, 2 dimes - 1 quarter - 25 pennies - 1 nickel, 2 dimes - 5 nickels - 5 pennies, 4 nickels - 5 pennies, 2 nickels, 1 dime -3 nickels, 1 dime -15 pennies, 1 dime -10 pennies, 1 nickel, 1 dime - 10 pennies, 3 nickels - 15 pennies, 2 nickels - 20 pennies, 1 nickel

Answer 3

Using pennies, nickels, dimes, quarters, half-dollars and dollar coins, there are 293 ways to make change for 1 US dollar.

Method 1:

Using pennies, nickels, dimes, quarters, half-dollar and dollar coins there are 293 ways to make change for one dollar. In general, to make change for d dollars using these coins there are (1 + d) (6 + 121 d + 362 d^2 + 310 d^3 + 80 d^4 )/ 6 ways. Without using the dollar coin, there are (6 + 55 h + 119 h2 + 95 h3 + 25 h4)/6 ways of making change for h dollars. For example, putting h=1 gives 50 ways of making change for fifty cents, or h=2 gives 292 ways of making change for a dollar.

Method 2:

Take the Taylor expansion of 1 over (1-x)*(1-x5)*(1-x10)*(1-x25)*(1-x50)*(1-x100), and jot down the coefficient of x100. This is the generating function for the ways to partition 100 into subsets of size 1, 5, 10, 25, 50, or 100, so there are 293 ways to make change for 1 US dollar.

Method 3:

Make a list as below. Using only pennies, nickels, dimes, and quarters, there are 242 ways to make a dollar; these begin with line 52.

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

Answer 4

Indisputable Tally of Combinations

Key: HD - Half Dollar ($0.50), Q - Quarter ($0.25), D - Dime ($0.10), N - Nickel ($0.05), P - Penny ($0.01)

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

Answer 5

The Data below is useless do not read or waist time the answer I could find is 13

I didn't put in the below information some assinide person did !

13

1.. H

2.. 2Q

3.. Q,2D,1N

4.. Q,2D,5P

5.. Q,1D,3N

6.. Q,1D,2N,5P

7.. Q,1D,1N,10P

8.. Q,1D,15P

9.. Q,5N

10 Q,4N,5P

11 Q,3N,10P

12 Q,2N.15P

13 Q,1N,20P

14 Q,25P

15 5D

16 4D,2N

17 4D,1N,5P

18 4D,10P

19 3D,4N

20 3D,3N,5P

21 3D,2N,10P

22 3D,1N,15P

23 3D,20P

24 2D,6N

25 2D,5N,5P

26 2D,4N,10P

27 2D,3N,15P

28 2D,2N,20P

29 2D,1N,25P

30 2D,30P

31 1D,8N

32 1D,7N,5P

33 1D,6N,10P

34 1D,5N,15P

35 1D,4N,20P

36 1D,3N,25P

37 1D,2N,30P

38 1D,1N,35P

39 1D,40P

40 10N

41 9N,5P

42 8N,10P

43 7N,15P

44 6N,20P

45 5N,25P

46 4N,30P

47 3N,35P

48 2N,40P

49 1N,45P

50 50P

Answer 6

1 dime, 1 nickel; 1 dime, 5 pennies; 3 nickels; 2 nickels, 5 pennies; 1 nickel, 10 pennies; 15 pennies. So there are six ways

Answer 7

There are nearly 300 ways to make change for a $20 bill.

Answer 8

6x5c

4x5c, 1x10c

2x5c, 2x10c

2x5c, 1x20c

1x10c, 1x20c

3x10c

Answer 9

1quartar

Answer 10

293