2. How many three-digit positive integers are there such that, the three digits of every integer, taken from left to right, form an arithmetic sequence?
(1 mark)
有多少個三位正整數的三個數字從左至右看時組成一個等差數列？
(1 分)
2. 45
2. The common difference may range from 4 to -4 . There are 7 numbers with common difference 1 (namely, $123,234, \ldots, 789$ ), and $5,3,1$ numbers with common difference $2,3,4$ respectively. It is then easy to see that there are $8,6,4,2$ numbers with common difference $1,-2,-3,-4$ respectively (the reverse of those numbers with common difference $1,2,3,4$, as well as those ending with 0 ). Finally there are 9 numbers with common difference 0 (namely, $111,222, \ldots, 999)$. Hence the answer is $7+5+3+1+8+6+4+2+9=45$.