Question

A three-digit number is called special if its digits form an increasing arithmetic sequence–that is, the difference between the first and second digit is the same as the difference between the second and third digit, and each digit is larger than the one to the left of it. For example, 567 is special, but 236, 111, 048, and 975 are not. How many three-digit special numbers exist?

Answer 1

Three-digit special numbers:

123, 234, 345, 456, 567, 678, 789.

ANSWER

there are 7 three-digit special numbers