mathematics for teachers

Question

A three‐digit number satisfies the following conditions: The digits are consecutive whole numbers in increasing order; the sum of each pair of digits is greater than 8 and less than 12; and the tens digit is an odd number. What is the number?

Answer 1

Since the 10s digit must be odd and the digits are consecutive whole numbers in increasing order AND

the first pair of digits must be greater than 8, the following have been ELIMINATED:

012

234

Still alive:

456

678

890

Each pair of consecutive digits however must be less than 12.

That eliminates 678 and 890

The answer is 456