+4622 A lucky integer is a positive integer which is divisible by the sum of its digits. What is the least positive multiple of 9 that is not a lucky integer?
+9481 The sum of the digits for each of the first ten multiples of 9 is 9 .
So the first 10 positive multiples of 9 must be lucky integers.
| 9 * 1 = 9 | and | 9/9 = 1 |
| 9 * 2 = 18 | and | 18/(1+8) = 2 |
| 9 * 3 = 27 | and | 27/(2+7) = 3 |
etc.
But....
9 * 11 = 99 and 99/( 9 + 9 ) = 5.5
So
99 is the least positive multiple of 9 that is not a lucky integer.
+9481 The sum of the digits for each of the first ten multiples of 9 is 9 .
So the first 10 positive multiples of 9 must be lucky integers.
| 9 * 1 = 9 | and | 9/9 = 1 |
| 9 * 2 = 18 | and | 18/(1+8) = 2 |
| 9 * 3 = 27 | and | 27/(2+7) = 3 |
etc.
But....
9 * 11 = 99 and 99/( 9 + 9 ) = 5.5
So
99 is the least positive multiple of 9 that is not a lucky integer.
