There are 292 ways to do it. While sitting in the back of the computer club meeting I decided I would write an APL function to list all the ways. I have listed all the methods in the chart below. Each vector shows the number of half-dollars, quarters, dimes, nickles, and pennies in that order. The first method is 100 pennies, the 2nd is a nickle and 95 pennies. Method 150 says you can do it with 1 quarter 1 dime 12 nickels and 5 pennies. Method 290 says you can do it with 1 half, 1 quarter, 2 dimes, and 1 nickle.
Not too sure how valuable this information is, but it took 0.469 seconds
for my slow computer using the slower version of APL to crank it out.
1] 0 0 0 0 100 |
74] 0 0 4 1 55 |
147] 0 1 1 9 20 |
220] 0 2 2 6 0 |
2] 0 0 0 1 95 |
75] 0 0 4 2 50 |
148] 0 1 1 10 15 |
221] 0 2 3 0 20 |
3] 0 0 0 2 90 |
76] 0 0 4 3 45 |
149] 0 1 1 11 10 |
222] 0 2 3 1 15 |
4] 0 0 0 3 85 |
77] 0 0 4 4 40 |
150] 0 1 1 12 5 |
223] 0 2 3 2 10 |
5] 0 0 0 4 80 |
78] 0 0 4 5 35 |
151] 0 1 1 13 0 |
224] 0 2 3 3 5 |
6] 0 0 0 5 75 |
79] 0 0 4 6 30 |
152] 0 1 2 0 55 |
225] 0 2 3 4 0 |
7] 0 0 0 6 70 |
80] 0 0 4 7 25 |
153] 0 1 2 1 50 |
226] 0 2 4 0 10 |
8] 0 0 0 7 65 |
81] 0 0 4 8 20 |
154] 0 1 2 2 45 |
227] 0 2 4 1 5 |
9] 0 0 0 8 60 |
82] 0 0 4 9 15 |
155] 0 1 2 3 40 |
228] 0 2 4 2 0 |
10] 0 0 0 9 55 |
83] 0 0 4 10 10 |
156] 0 1 2 4 35 |
229] 0 2 5 0 0 |
11] 0 0 0 10 50 |
84] 0 0 4 11 5 |
157] 0 1 2 5 30 |
230] 0 3 0 0 25 |
12] 0 0 0 11 45 |
85] 0 0 4 12 0 |
158] 0 1 2 6 25 |
231] 0 3 0 1 20 |
13] 0 0 0 12 40 |
86] 0 0 5 0 50 |
159] 0 1 2 7 20 |
232] 0 3 0 2 15 |
14] 0 0 0 13 35 |
87] 0 0 5 1 45 |
160] 0 1 2 8 15 |
233] 0 3 0 3 10 |
15] 0 0 0 14 30 |
88] 0 0 5 2 40 |
161] 0 1 2 9 10 |
234] 0 3 0 4 5 |
16] 0 0 0 15 25 |
89] 0 0 5 3 35 |
162] 0 1 2 10 5 |
235] 0 3 0 5 0 |
17] 0 0 0 16 20 |
90] 0 0 5 4 30 |
163] 0 1 2 11 0 |
236] 0 3 1 0 15 |
18] 0 0 0 17 15 |
91] 0 0 5 5 25 |
164] 0 1 3 0 45 |
237] 0 3 1 1 10 |
19] 0 0 0 18 10 |
92] 0 0 5 6 20 |
165] 0 1 3 1 40 |
238] 0 3 1 2 5 |
20] 0 0 0 19 5 |
93] 0 0 5 7 15 |
166] 0 1 3 2 35 |
239] 0 3 1 3 0 |
21] 0 0 0 20 0 |
94] 0 0 5 8 10 |
167] 0 1 3 3 30 |
240] 0 3 2 0 5 |
22] 0 0 1 0 90 |
95] 0 0 5 9 5 |
168] 0 1 3 4 25 |
241] 0 3 2 1 0 |
23] 0 0 1 1 85 |
96] 0 0 5 10 0 |
169] 0 1 3 5 20 |
242] 0 4 0 0 0 |
24] 0 0 1 2 80 |
97] 0 0 6 0 40 |
170] 0 1 3 6 15 |
243] 1 0 0 0 50 |
25] 0 0 1 3 75 |
98] 0 0 6 1 35 |
171] 0 1 3 7 10 |
244] 1 0 0 1 45 |
26] 0 0 1 4 70 |
99] 0 0 6 2 30 |
172] 0 1 3 8 5 |
245] 1 0 0 2 40 |
27] 0 0 1 5 65 |
100] 0 0 6 3 25 |
173] 0 1 3 9 0 |
246] 1 0 0 3 35 |
28] 0 0 1 6 60 |
101] 0 0 6 4 20 |
174] 0 1 4 0 35 |
247] 1 0 0 4 30 |
29] 0 0 1 7 55 |
102] 0 0 6 5 15 |
175] 0 1 4 1 30 |
248] 1 0 0 5 25 |
30] 0 0 1 8 50 |
103] 0 0 6 6 10 |
176] 0 1 4 2 25 |
249] 1 0 0 6 20 |
31] 0 0 1 9 45 |
104] 0 0 6 7 5 |
177] 0 1 4 3 20 |
250] 1 0 0 7 15 |
32] 0 0 1 10 40 |
105] 0 0 6 8 0 |
178] 0 1 4 4 15 |
251] 1 0 0 8 10 |
33] 0 0 1 11 35 |
106] 0 0 7 0 30 |
179] 0 1 4 5 10 |
252] 1 0 0 9 5 |
34] 0 0 1 12 30 |
107] 0 0 7 1 25 |
180] 0 1 4 6 5 |
253] 1 0 0 10 0 |
35] 0 0 1 13 25 |
108] 0 0 7 2 20 |
181] 0 1 4 7 0 |
254] 1 0 1 0 40 |
36] 0 0 1 14 20 |
109] 0 0 7 3 15 |
182] 0 1 5 0 25 |
255] 1 0 1 1 35 |
37] 0 0 1 15 15 |
110] 0 0 7 4 10 |
183] 0 1 5 1 20 |
256] 1 0 1 2 30 |
38] 0 0 1 16 10 |
111] 0 0 7 5 5 |
184] 0 1 5 2 15 |
257] 1 0 1 3 25 |
39] 0 0 1 17 5 |
112] 0 0 7 6 0 |
185] 0 1 5 3 10 |
258] 1 0 1 4 20 |
40] 0 0 1 18 0 |
113] 0 0 8 0 20 |
186] 0 1 5 4 5 |
259] 1 0 1 5 15 |
41] 0 0 2 0 80 |
114] 0 0 8 1 15 |
187] 0 1 5 5 0 |
260] 1 0 1 6 10 |
42] 0 0 2 1 75 |
115] 0 0 8 2 10 |
188] 0 1 6 0 15 |
261] 1 0 1 7 5 |
43] 0 0 2 2 70 |
116] 0 0 8 3 5 |
189] 0 1 6 1 10 |
262] 1 0 1 8 0 |
44] 0 0 2 3 65 |
117] 0 0 8 4 0 |
190] 0 1 6 2 5 |
263] 1 0 2 0 30 |
45] 0 0 2 4 60 |
118] 0 0 9 0 10 |
191] 0 1 6 3 0 |
264] 1 0 2 1 25 |
46] 0 0 2 5 55 |
119] 0 0 9 1 5 |
192] 0 1 7 0 5 |
265] 1 0 2 2 20 |
47] 0 0 2 6 50 |
120] 0 0 9 2 0 |
193] 0 1 7 1 0 |
266] 1 0 2 3 15 |
48] 0 0 2 7 45 |
121] 0 0 10 0 0 |
194] 0 2 0 0 50 |
267] 1 0 2 4 10 |
49] 0 0 2 8 40 |
122] 0 1 0 0 75 |
195] 0 2 0 1 45 |
268] 1 0 2 5 5 |
50] 0 0 2 9 35 |
123] 0 1 0 1 70 |
196] 0 2 0 2 40 |
269] 1 0 2 6 0 |
51] 0 0 2 10 30 |
124] 0 1 0 2 65 |
197] 0 2 0 3 35 |
270] 1 0 3 0 20 |
52] 0 0 2 11 25 |
125] 0 1 0 3 60 |
198] 0 2 0 4 30 |
271] 1 0 3 1 15 |
53] 0 0 2 12 20 |
126] 0 1 0 4 55 |
199] 0 2 0 5 25 |
272] 1 0 3 2 10 |
54] 0 0 2 13 15 |
127] 0 1 0 5 50 |
200] 0 2 0 6 20 |
273] 1 0 3 3 5 |
55] 0 0 2 14 10 |
128] 0 1 0 6 45 |
201] 0 2 0 7 15 |
274] 1 0 3 4 0 |
56] 0 0 2 15 5 |
129] 0 1 0 7 40 |
202] 0 2 0 8 10 |
275] 1 0 4 0 10 |
57] 0 0 2 16 0 |
130] 0 1 0 8 35 |
203] 0 2 0 9 5 |
276] 1 0 4 1 5 |
58] 0 0 3 0 70 |
131] 0 1 0 9 30 |
204] 0 2 0 10 0 |
277] 1 0 4 2 0 |
59] 0 0 3 1 65 |
132] 0 1 0 10 25 |
205] 0 2 1 0 40 |
278] 1 0 5 0 0 |
60] 0 0 3 2 60 |
133] 0 1 0 11 20 |
206] 0 2 1 1 35 |
279] 1 1 0 0 25 |
61] 0 0 3 3 55 |
134] 0 1 0 12 15 |
207] 0 2 1 2 30 |
280] 1 1 0 1 20 |
62] 0 0 3 4 50 |
135] 0 1 0 13 10 |
208] 0 2 1 3 25 |
281] 1 1 0 2 15 |
63] 0 0 3 5 45 |
136] 0 1 0 14 5 |
209] 0 2 1 4 20 |
282] 1 1 0 3 10 |
64] 0 0 3 6 40 |
137] 0 1 0 15 0 |
210] 0 2 1 5 15 |
283] 1 1 0 4 5 |
65] 0 0 3 7 35 |
138] 0 1 1 0 65 |
211] 0 2 1 6 10 |
284] 1 1 0 5 0 |
66] 0 0 3 8 30 |
139] 0 1 1 1 60 |
212] 0 2 1 7 5 |
285] 1 1 1 0 15 |
67] 0 0 3 9 25 |
140] 0 1 1 2 55 |
213] 0 2 1 8 0 |
286] 1 1 1 1 10 |
68] 0 0 3 10 20 |
141] 0 1 1 3 50 |
214] 0 2 2 0 30 |
287] 1 1 1 2 5 |
69] 0 0 3 11 15 |
142] 0 1 1 4 45 |
215] 0 2 2 1 25 |
288] 1 1 1 3 0 |
70] 0 0 3 12 10 |
143] 0 1 1 5 40 |
216] 0 2 2 2 20 |
289] 1 1 2 0 5 |
71] 0 0 3 13 5 |
144] 0 1 1 6 35 |
217] 0 2 2 3 15 |
290] 1 1 2 1 0 |
72] 0 0 3 14 0 |
145] 0 1 1 7 30 |
218] 0 2 2 4 10 |
291] 1 2 0 0 0 |
73] 0 0 4 0 60 |
146] 0 1 1 8 25 |
219] 0 2 2 5 5 |
292] 2 0 0 0 0 |
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