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 Year Yearn 3 (Posted on 2016-04-05)
It is observed that 2016 = 16*126. In other words 2016 can be written as: AC*ABC where each of A, B and C is a distinct base ten digit with A being a nonzero digit.

Determine the next three positive integers having this property. What are the preceding three positive integers with this property?

 No Solution Yet Submitted by K Sengupta No Rating

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 computer solution Comment 1 of 1
First starting with 2016 and going forward, then a set going backward.  Asterisks marke a second way of producing the same number.  "Next three" and "preceding three" such numbers are bolded. The "preceding three" include two ways for one of them, so four lines are bolded there.

2016 16 126
2025 15 135
2064 12 172
2071 19 109
2119 13 163
2156 14 154
2159 17 127
2175 15 145
2176 16 136
2184 12 182
2249 13 173
2296 14 164
2304 12 192
2304 18 128 *
2329 17 137
2336 16 146
2379 13 183
2436 14 174
2451 19 129
2475 15 165
2484 18 138
2496 16 156
2499 17 147
2509 13 193
2576 14 184
2625 15 175
2641 19 139
2664 18 148
2669 17 157
2716 14 194
2775 15 185
2816 16 176
2831 19 149
2839 17 167
2844 18 158
2925 15 195
2976 16 186
3021 19 159
3024 18 168
3136 16 196
3179 17 187
3204 18 178
3211 19 169
3349 17 197
3401 19 179
3564 18 198
3591 19 189
4200 20 210
4221 21 201
4600 20 230
4669 23 203
4800 20 240
4851 21 231
4896 24 204
4899 23 213
5000 20 250
5061 21 241
5125 25 205
5136 24 214
5200 20 260
5271 21 251
5356 26 206
5375 25 215
5400 20 270
5481 21 261
5589 23 243
5589 27 207 *
5600 20 280
5616 24 234
5616 26 216 *
5691 21 271
5800 20 290
5819 23 253
5824 28 208
5859 27 217
5875 25 235
5901 21 281
6049 23 263
6061 29 209
6096 24 254
6104 28 218
6111 21 291
6125 25 245
6136 26 236
6279 23 273
6336 24 264
6351 29 219
6396 26 246
6399 27 237
6509 23 283
6576 24 274
6625 25 265
6656 26 256
6664 28 238
6669 27 247
6739 23 293
6816 24 284
6875 25 275
6931 29 239
6939 27 257
6944 28 248
7056 24 294
7125 25 285
7176 26 276
7209 27 267
7221 29 249
7224 28 258
7375 25 295
7436 26 286
7504 28 268
7511 29 259
7696 26 296
7749 27 287
7784 28 278
7801 29 269
8019 27 297
8091 29 279
8344 28 298
8381 29 289
9300 30 310
9331 31 301
9600 30 320
9664 32 302
9951 31 321
9984 32 312

2016 16 126
1989 13 153
1944 12 162
1944 18 108 *
1900 10 190
1876 14 134
1875 15 125
1859 13 143
1824 12 152
1819 17 107
1800 10 180
1736 14 124
1704 12 142
1700 10 170
1696 16 106
1600 10 160
1599 13 123
1584 12 132
1575 15 105
1500 10 150
1456 14 104
1400 10 140
1339 13 103
1300 10 130
1224 12 102
1200 10 120

DefDbl A-Z
Dim crlf\$

Form1.Visible = True

Text1.Text = ""
crlf = Chr\$(13) + Chr\$(10)

For y = 2016 To 9999
For dvr = 10 To 98
DoEvents
If dvr \ 10 <> dvr Mod 10 Then
q = y / dvr
If q = Int(q) Then
If (q \ 10) Mod 10 <> dvr Mod 10 And (q \ 10) Mod 10 <> dvr \ 10 Then
If q \ 100 = dvr \ 10 And q Mod 10 = dvr Mod 10 Then
Text1.Text = Text1.Text & y & Str(dvr) & Str(q)
If y = prev Then Text1.Text = Text1.Text & " *"
prev = y
Text1.Text = Text1.Text & crlf
End If
End If
End If
End If
Next
Next y

Text1.Text = Text1.Text & crlf

For y = 2016 To 1000 Step -1
For dvr = 10 To 98
If dvr \ 10 <> dvr Mod 10 Then
q = y / dvr
If q = Int(q) Then
If (q \ 10) Mod 10 <> dvr Mod 10 And (q \ 10) Mod 10 <> dvr \ 10 Then
If q \ 100 = dvr \ 10 And q Mod 10 = dvr Mod 10 Then
Text1.Text = Text1.Text & y & Str(dvr) & Str(q)
If y = prev Then Text1.Text = Text1.Text & " *"
prev = y
Text1.Text = Text1.Text & crlf
End If
End If
End If
End If
Next
Next y

Text1.Text = Text1.Text & crlf & " done"

End Sub

 Posted by Charlie on 2016-04-05 10:22:40

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