.
Let n be the middle number of the three consecutive odd integers.
Then the first number is (n-2), while the third integer is (n+2).
The sum of the three numbers is 171:
(n-2) + n + (n+2) = 171, or
3n = 171,
which gives
n = 171/3 = 57.
Thus the numbers are 55, 57 and 59. ANSWER
----------------
The lesson to learn from my solution is THIS :
The sum of three consecutive odd integer numbers is three times the middle number.
Another form of this statement is THIS :
If you are given the sum of three consecutive odd integer numbers, then the middle number is (one third) of the sum.
Therefore, by knowing this property, you can solve many other similar problems MOMENTARILY (and mentally, without using equations) (!)
As if you are a magician ( ! ! )