Expert: Pawan Musale - 9/14/2009

Question
xyz
+xyz
+xyz
-----
zzz  then what is x

or ( xyz+xyz+xyz=zzz than what is X )

Answer
Sudhir,

Let us solve this problem/puzzle.

              xyz
        +     xyz
        +     xyz
        -----------------
              zzz

We know that zzz means a 3 digit number with same digit in all three places. And xyz is a three digit number with different digits in all three places. Now xyz is added three times. Means we can write the given equation in simple format as:

3* xyz = zzz
xyz = zzz/3 ------------ #1

Now zzz can have any value from 111, 222, 333 till 999. So you can take one number each, divide it by 3 and check if it fits in the expression.

Let us do it for zzz = 111.

From equation #1 above,
xyz = 111/3 = 37 = 037. so xyz = 037. But in this case, last digit comes out to be 7 and not 1 (z). Hence this is not valid number.

Likewise we can test it for all nine numbers. But there is really no need of doing it.

Since xyz has the digit z at its unit place, we have to find a number (zzz) which, after divided by 3, will give the same digit at units place.

There is only one such number 555 which after divided by 3, gives 185 and this number is having 5 at it unit's place.

So

                         185
                       + 185
                       + 185
                     -------------
                         555

So your x = 1.

If you do not fully understand this solution, then please let me know. I will tell you other method to solve this. There are multiple ways in which this can be solved. This one was the simplest one. Do let me know if this is clear or not.

All the best for your studies. :)

Regards,
Pawan