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If the digit '1' occupies the hundreds place then the other two digits total 8.
108, 117, 126, 135, 144, 153, 162, 171, 180 (9 three digit numbers)
Similarly with '2 in the hundreds position the the remaining digits total 7.
207, 216, 225, 234, 243, 252, 261, 270 (8 three digit numbers)
When the remaining numbers 3 to 9 are set as the lead digit then the number of three digit numbers formed decreases by one each time.
The final total of such numbers is, 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 45.
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