If the 9 digit number is written as ABCDEFGHI then
3ABC = GHI
GHI  ABC = DEF
As GHI is still a 3digit number then ABC must be less than 333. so A is 1,2 or 3 and G can't be 1 or 2.
If C is 5 then I is 5 but each digit must be different so C & I are not 5.
I then wrote down the numbers 1 to 99 (BC) and then multiplied each number by 3 (HI) and only looking at the last two digits of HI.
I then went through and eliminated the numbers which had duplicates or the number 0 and came up with 34 possibilities:
BC HI
12 36
16 48
18 54
19 57
21 63
23 69
26 78
27 81
29 87
32 96
38 114
39 117
41 123
43 129
46 138
54 162
58 174
61 183
63 189
64 192
72 216
73 219
76 228
78 234
81 243
82 246
83 249
84 252
86 258
87 261
89 267
91 273
92 276
94 282
I added a third column showing the difference between the two numbers and then went through putting the number 1, 2 & 3 before the two digit number BC and seeing if all three sets of numbers had different digits and I came up with the follwing 4 solutions:
219 438 657
327 654 981
273 546 819
192 384 576

Posted by Lisa
on 20050722 14:09:09 