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Question 835054: Using every one of the digits 1-9 only once, make an addition problem using only 3-digit numbers. I made a systematic list of all three digit answers from 981 to 459 and could find addends to sum to all of those answers except for 864, 765, and 756. Why don't these 3 work and why don't numbers in the 300s work?
Answer by Edwin McCravy(20060)   (Show Source):
You can put this solution on YOUR website!
There is no system that will guarantee that
you don't use any digits more than once.
You can use any of these 168 ways. I found
these by a computer program.
1. 124 + 659 = 783
2. 125 + 739 = 864
3. 127 + 359 = 486
4. 127 + 368 = 495
5. 128 + 367 = 495
6. 128 + 439 = 567
7. 129 + 357 = 486
8. 129 + 438 = 567
9. 129 + 654 = 783
10. 129 + 735 = 864
11. 134 + 658 = 792
12. 135 + 729 = 864
13. 138 + 429 = 567
14. 138 + 654 = 792
15. 139 + 428 = 567
16. 139 + 725 = 864
17. 142 + 596 = 738
18. 142 + 695 = 837
19. 143 + 586 = 729
20. 145 + 692 = 837
21. 146 + 583 = 729
22. 146 + 592 = 738
23. 152 + 487 = 639
24. 152 + 784 = 936
25. 154 + 629 = 783
26. 154 + 638 = 792
27. 154 + 782 = 936
28. 157 + 329 = 486
29. 157 + 482 = 639
30. 158 + 634 = 792
31. 159 + 327 = 486
32. 159 + 624 = 783
33. 162 + 387 = 549
34. 162 + 783 = 945
35. 163 + 782 = 945
36. 167 + 328 = 495
37. 167 + 382 = 549
38. 168 + 327 = 495
39. 173 + 286 = 459
40. 173 + 295 = 468
41. 175 + 293 = 468
42. 176 + 283 = 459
43. 182 + 367 = 549
44. 182 + 394 = 576
45. 182 + 457 = 639
46. 182 + 493 = 675
47. 182 + 754 = 936
48. 182 + 763 = 945
49. 183 + 276 = 459
50. 183 + 492 = 675
51. 183 + 546 = 729
52. 183 + 762 = 945
53. 184 + 392 = 576
54. 184 + 752 = 936
55. 186 + 273 = 459
56. 186 + 543 = 729
57. 187 + 362 = 549
58. 187 + 452 = 639
59. 192 + 384 = 576
60. 192 + 483 = 675
61. 192 + 546 = 738
62. 192 + 645 = 837
63. 193 + 275 = 468
64. 193 + 482 = 675
65. 194 + 382 = 576
66. 195 + 273 = 468
67. 195 + 642 = 837
68. 196 + 542 = 738
69. 214 + 569 = 783
70. 214 + 659 = 873
71. 215 + 478 = 693
72. 215 + 748 = 963
73. 216 + 378 = 594
74. 216 + 738 = 954
75. 218 + 349 = 567
76. 218 + 376 = 594
77. 218 + 439 = 657
78. 218 + 475 = 693
79. 218 + 736 = 954
80. 218 + 745 = 963
81. 219 + 348 = 567
82. 219 + 438 = 657
83. 219 + 564 = 783
84. 219 + 654 = 873
85. 234 + 657 = 891
86. 235 + 746 = 981
87. 236 + 718 = 954
88. 236 + 745 = 981
89. 237 + 654 = 891
90. 238 + 419 = 657
91. 238 + 716 = 954
92. 239 + 418 = 657
93. 241 + 596 = 837
94. 243 + 576 = 819
95. 243 + 675 = 918
96. 245 + 673 = 918
97. 245 + 718 = 963
98. 245 + 736 = 981
99. 246 + 573 = 819
100. 246 + 591 = 837
101. 246 + 735 = 981
102. 248 + 319 = 567
103. 248 + 715 = 963
104. 249 + 318 = 567
105. 251 + 397 = 648
106. 254 + 619 = 873
107. 254 + 637 = 891
108. 257 + 391 = 648
109. 257 + 634 = 891
110. 259 + 614 = 873
111. 264 + 519 = 783
112. 269 + 514 = 783
113. 271 + 593 = 864
114. 271 + 683 = 954
115. 273 + 546 = 819
116. 273 + 591 = 864
117. 273 + 645 = 918
118. 273 + 681 = 954
119. 275 + 418 = 693
120. 275 + 643 = 918
121. 276 + 318 = 594
122. 276 + 543 = 819
123. 278 + 316 = 594
124. 278 + 415 = 693
125. 281 + 394 = 675
126. 281 + 673 = 954
127. 283 + 671 = 954
128. 284 + 391 = 675
129. 291 + 357 = 648
130. 291 + 384 = 675
131. 291 + 546 = 837
132. 291 + 573 = 864
133. 293 + 571 = 864
134. 294 + 381 = 675
135. 296 + 541 = 837
136. 297 + 351 = 648
137. 314 + 658 = 972
138. 317 + 529 = 846
139. 317 + 628 = 945
140. 318 + 627 = 945
141. 318 + 654 = 972
142. 319 + 527 = 846
143. 324 + 567 = 891
144. 324 + 657 = 981
145. 327 + 519 = 846
146. 327 + 564 = 891
147. 327 + 618 = 945
148. 327 + 654 = 981
149. 328 + 617 = 945
150. 329 + 517 = 846
151. 341 + 586 = 927
152. 342 + 576 = 918
153. 346 + 572 = 918
154. 346 + 581 = 927
155. 352 + 467 = 819
156. 354 + 618 = 972
157. 354 + 627 = 981
158. 357 + 462 = 819
159. 357 + 624 = 981
160. 358 + 614 = 972
161. 362 + 457 = 819
162. 364 + 527 = 891
163. 367 + 452 = 819
164. 367 + 524 = 891
165. 372 + 546 = 918
166. 376 + 542 = 918
167. 381 + 546 = 927
168. 386 + 541 = 927
Edwin
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