Question 460851
You could solve this with guesswork or mathematically, so let us look at it both ways.


Guesswork:


Three numbers in succession


1, 2, 3: too low since 1 + 2 + 3 = 6;
2, 3, 4: too low since 2 + 3 + 4 = 9;
3, 4, 5: okay since 3 + 4 + 5 = 12
4, 5, 6: okay since 4 + 5 + 6 = 15
5, 6, 7: okay since 5 + 6 + 7 = 18
6, 7, 8: too high since 6 + 7 + 8 = 21


We can see that we have three to choose form but the ten’s must be odd, so the only solution is 456.


Mathematically:


Let the three numbers be a - 1, a, a + 1 where a is the ten digit


The sum of the three digits is 3a which has to be between 10 and 20, so 3a = 12, 15 or 18 giving a = 4, 5 or 6.


The only odd value for a is 5, so the three digit number we have is 456.