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let the number be abcd (i.e. 1000a + 100b + 10c + d)
therefore, the condition imposed means : (10a + b) + (10c + d) = (10b + c) ====> 10a + d = 9 ( b - c)
therefore, 10a + d should be a number (one or 2 digit) divisible by 9 ====> it can be 9, 18, 27, 36, 45, 54, 63, 72 and 81
while the corresponding b-c should be 1,2, 3, 4, 5, 6, 7, 8 and 9
now we can write the digits down using this information e.g. for ab= 18, the combinations are 1978, 1868, 1758, 1648, 1538, 1428, 1318, 1208
the total number of such answers = 1+2+...+9=45
(excluding 0000 of course)
therefore, the condition imposed means : (10a + b) + (10c + d) = (10b + c) ====> 10a + d = 9 ( b - c)
therefore, 10a + d should be a number (one or 2 digit) divisible by 9 ====> it can be 9, 18, 27, 36, 45, 54, 63, 72 and 81
while the corresponding b-c should be 1,2, 3, 4, 5, 6, 7, 8 and 9
now we can write the digits down using this information e.g. for ab= 18, the combinations are 1978, 1868, 1758, 1648, 1538, 1428, 1318, 1208
the total number of such answers = 1+2+...+9=45
(excluding 0000 of course)