using numbers from 0 to 9, list all 4 digit numbers that add up to 19

Question

list all combo's of 4 digit numbers that add up to 19 using all numbers  from 0 to 9

Answer 1

Well, there are 660 of them.


This Answer Forum will not let me “list all 4 digit numbers that add up to 19;” it will truncate the list when it gets full.


However, you should consider some logic necessary to determine that there are 660 possibilities:
   -  suppose the first number is 0
        -  now suppose the second number is 0
                   How many combinations are left to add up to 19?    (why do you think they picked 19?)
    -  suppose the first number is 0
        - now suppose the second number is 1
                   How many combinations are left to add up to 19?
   -  suppose the first number is 0
         - now suppose the second number is 2
                   How many combinations are left to add up to 19?
   . . .
      See some pattern yet??
   . . .
      Oh,.., watch happens when the first two numbers start to get larger (and the last two look like the reverse of the first two, and finally get to be 1 and 0 !!     This chart looks like a triangle.

When you add up all the values (don’t get discouraged; there aren’t all that many), you should get 660.

To see a pattern and to check some work, here is the list (as far as the Answers Forum box allows):

1: 0 1 9 9
2: 0 2 8 9
3: 0 2 9 8
4: 0 3 7 9
5: 0 3 8 8
6: 0 3 9 7
7: 0 4 6 9
8: 0 4 7 8
9: 0 4 8 7
10: 0 4 9 6
11: 0 5 5 9
12: 0 5 6 8
13: 0 5 7 7
14: 0 5 8 6
15: 0 5 9 5
16: 0 6 4 9
17: 0 6 5 8
18: 0 6 6 7
19: 0 6 7 6
20: 0 6 8 5
21: 0 6 9 4
22: 0 7 3 9
23: 0 7 4 8
24: 0 7 5 7
25: 0 7 6 6
26: 0 7 7 5
27: 0 7 8 4
28: 0 7 9 3
29: 0 8 2 9
30: 0 8 3 8
31: 0 8 4 7
32: 0 8 5 6
33: 0 8 6 5
34: 0 8 7 4
35: 0 8 8 3
36: 0 8 9 2
37: 0 9 1 9
38: 0 9 2 8
39: 0 9 3 7
40: 0 9 4 6
41: 0 9 5 5
42: 0 9 6 4
43: 0 9 7 3
44: 0 9 8 2
45: 0 9 9 1
46: 1 0 9 9
47: 1 1 8 9
48: 1 1 9 8
49: 1 2 7 9
50: 1 2 8 8
51: 1 2 9 7
52: 1 3 6 9
53: 1 3 7 8
54: 1 3 8 7
55: 1 3 9 6
56: 1 4 5 9
57: 1 4 6 8
58: 1 4 7 7
59: 1 4 8 6
60: 1 4 9 5
61: 1 5 4 9
62: 1 5 5 8
63: 1 5 6 7
64: 1 5 7 6
65: 1 5 8 5
66: 1 5 9 4
67: 1 6 3 9
68: 1 6 4 8
69: 1 6 5 7
70: 1 6 6 6
71: 1 6 7 5
72: 1 6 8 4
73: 1 6 9 3
74: 1 7 2 9
75: 1 7 3 8
76: 1 7 4 7
77: 1 7 5 6
78: 1 7 6 5
79: 1 7 7 4
80: 1 7 8 3
81: 1 7 9 2
82: 1 8 1 9
83: 1 8 2 8
84: 1 8 3 7
85: 1 8 4 6
86: 1 8 5 5
87: 1 8 6 4
88: 1 8 7 3
89: 1 8 8 2
90: 1 8 9 1
91: 1 9 0 9
92: 1 9 1 8
93: 1 9 2 7
94: 1 9 3 6
95: 1 9 4 5
96: 1 9 5 4
97: 1 9 6 3
98: 1 9 7 2
99: 1 9 8 1
100: 1 9 9 0
101: 2 0 8 9
102: 2 0 9 8
103: 2 1 7 9
104: 2 1 8 8
105: 2 1 9 7
106: 2 2 6 9
107: 2 2 7 8
108: 2 2 8 7
109: 2 2 9 6
110: 2 3 5 9
111: 2 3 6 8
112: 2 3 7 7
113: 2 3 8 6
114: 2 3 9 5
115: 2 4 4 9
116: 2 4 5 8
117: 2 4 6 7
118: 2 4 7 6
119: 2 4 8 5
120: 2 4 9 4
121: 2 5 3 9
122: 2 5 4 8
123: 2 5 5 7
124: 2 5 6 6
125: 2 5 7 5
126: 2 5 8 4
127: 2 5 9 3
128: 2 6 2 9
129: 2 6 3 8
130: 2 6 4 7
131: 2 6 5 6
132: 2 6 6 5
133: 2 6 7 4
134: 2 6 8 3
135: 2 6 9 2
136: 2 7 1 9
137: 2 7 2 8
138: 2 7 3 7
139: 2 7 4 6
140: 2 7 5 5
141: 2 7 6 4
142: 2 7 7 3
143: 2 7 8 2
144: 2 7 9 1
145: 2 8 0 9
146: 2 8 1 8
147: 2 8 2 7
148: 2 8 3 6
149: 2 8 4 5
150: 2 8 5 4
151: 2 8 6 3
152: 2 8 7 2
153: 2 8 8 1
154: 2 8 9 0
155: 2 9 0 8
156: 2 9 1 7
157: 2 9 2 6
158: 2 9 3 5
159: 2 9 4 4
160: 2 9 5 3
161: 2 9 6 2
162: 2 9 7 1
163: 2 9 8 0
164: 3 0 7 9
165: 3 0 8 8
166: 3 0 9 7
167: 3 1 6 9
168: 3 1 7 8
169: 3 1 8 7
170: 3 1 9 6
171: 3 2 5 9
172: 3 2 6 8
173: 3 2 7 7
174: 3 2 8 6
175: 3 2 9 5
176: 3 3 4 9
177: 3 3 5 8
178: 3 3 6 7
179: 3 3 7 6
180: 3 3 8 5
181: 3 3 9 4
182: 3 4 3 9
183: 3 4 4 8
184: 3 4 5 7
185: 3 4 6 6
186: 3 4 7 5
187: 3 4 8 4
188: 3 4 9 3
189: 3 5 2 9
190: 3 5 3 8
191: 3 5 4 7
192: 3 5 5 6
193: 3 5 6 5
194: 3 5 7 4
195: 3 5 8 3
196: 3 5 9 2
197: 3 6 1 9
198: 3 6 2 8
199: 3 6 3 7
200: 3 6 4 6
201: 3 6 5 5
202: 3 6 6 4
203: 3 6 7 3
204: 3 6 8 2
205: 3 6 9 1
206: 3 7 0 9
207: 3 7 1 8
208: 3 7 2 7
209: 3 7 3 6
210: 3 7 4 5
211: 3 7 5 4
212: 3 7 6 3
213: 3 7 7 2
214: 3 7 8 1
215: 3 7 9 0
216: 3 8 0 8
217: 3 8 1 7
218: 3 8 2 6
219: 3 8 3 5
220: 3 8 4 4
221: 3 8 5 3
222: 3 8 6 2
223: 3 8 7 1
224: 3 8 8 0
225: 3 9 0 7
226: 3 9 1 6
227: 3 9 2 5
228: 3 9 3 4
229: 3 9 4 3
230: 3 9 5 2
231: 3 9 6 1
232: 3 9 7 0



. . .

 

529: 8 0 2 9
530: 8 0 3 8
531: 8 0 4 7
532: 8 0 5 6
533: 8 0 6 5
534: 8 0 7 4
535: 8 0 8 3
536: 8 0 9 2
537: 8 1 1 9
538: 8 1 2 8
539: 8 1 3 7
540: 8 1 4 6
541: 8 1 5 5
542: 8 1 6 4
543: 8 1 7 3
544: 8 1 8 2
545: 8 1 9 1
546: 8 2 0 9
547: 8 2 1 8
548: 8 2 2 7
549: 8 2 3 6
550: 8 2 4 5
551: 8 2 5 4
552: 8 2 6 3
553: 8 2 7 2
554: 8 2 8 1
555: 8 2 9 0
556: 8 3 0 8
557: 8 3 1 7
558: 8 3 2 6
559: 8 3 3 5
560: 8 3 4 4
561: 8 3 5 3
562: 8 3 6 2
563: 8 3 7 1
564: 8 3 8 0
565: 8 4 0 7
566: 8 4 1 6
567: 8 4 2 5
568: 8 4 3 4
569: 8 4 4 3
570: 8 4 5 2
571: 8 4 6 1
572: 8 4 7 0
573: 8 5 0 6
574: 8 5 1 5
575: 8 5 2 4
576: 8 5 3 3
577: 8 5 4 2
578: 8 5 5 1
579: 8 5 6 0
580: 8 6 0 5
581: 8 6 1 4
582: 8 6 2 3
583: 8 6 3 2
584: 8 6 4 1
585: 8 6 5 0
586: 8 7 0 4
587: 8 7 1 3
588: 8 7 2 2
589: 8 7 3 1
590: 8 7 4 0
591: 8 8 0 3
592: 8 8 1 2
593: 8 8 2 1
594: 8 8 3 0
595: 8 9 0 2
596: 8 9 1 1
597: 8 9 2 0
598: 9 0 1 9
599: 9 0 2 8
600: 9 0 3 7
601: 9 0 4 6
602: 9 0 5 5
603: 9 0 6 4
604: 9 0 7 3
605: 9 0 8 2
606: 9 0 9 1
607: 9 1 0 9
608: 9 1 1 8
609: 9 1 2 7
610: 9 1 3 6
611: 9 1 4 5
612: 9 1 5 4
613: 9 1 6 3
614: 9 1 7 2
615: 9 1 8 1
616: 9 1 9 0
617: 9 2 0 8
618: 9 2 1 7
619: 9 2 2 6
620: 9 2 3 5
621: 9 2 4 4
622: 9 2 5 3
623: 9 2 6 2
624: 9 2 7 1
625: 9 2 8 0
626: 9 3 0 7
627: 9 3 1 6
628: 9 3 2 5
629: 9 3 3 4
630: 9 3 4 3
631: 9 3 5 2
632: 9 3 6 1
633: 9 3 7 0
634: 9 4 0 6
635: 9 4 1 5
636: 9 4 2 4
637: 9 4 3 3
638: 9 4 4 2
639: 9 4 5 1
640: 9 4 6 0
641: 9 5 0 5
642: 9 5 1 4
643: 9 5 2 3
644: 9 5 3 2
645: 9 5 4 1
646: 9 5 5 0
647: 9 6 0 4
648: 9 6 1 3
649: 9 6 2 2
650: 9 6 3 1
651: 9 6 4 0
652: 9 7 0 3
653: 9 7 1 2
654: 9 7 2 1
655: 9 7 3 0
656: 9 8 0 2
657: 9 8 1 1
658: 9 8 2 0
659: 9 9 0 1
660: 9 9 1 0