NWA-PCUG Newsletter Article, August 2004
How Many Ways To Break A $?
by John Clark, Webmaster
rcmahq@nwark.com
(click to email author)


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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