Wow...I don't know how it works, but it guessed my number every time!!
If you dont want to know how it is done don't read any further.
When you mix up the numbers and subtract the two numbers,your answer will have the sum of the digits to be a multiple of 9.
If your resultant answer was 1233 1+2+3+3=9 and you circled 3,you could write 123,132.213,231.312 or 321. But if you added the 3 digit you would get 6 >now subtract it from 9 and you get 3,the number you circled.
If you resultant subtraction digits were over 9 ,you would subtract from 18 or 27 ex resultant # was 9873 (9+8+7+3=27). circle one of the number say 9,then 8+7+3=18/ 37-18=9 the number circled. This is also why you were told not to circle 0.
Since if you answer was 8073 and you circled 0 your remaining numbers would add up to 18 and you wouldnt know to subtract from 18 or 27.
Wouldn't the same principle apply?
The sum of the digits, added again and again until only one digit remains, must be 9 (18 ... 1+8 = 9; 27 ... 2+7 = 9). Therefore, if you circled 0 (zero), the remaining digits would add to 9 (nine) -- the only [non] number to add to 9 (nine) and still get 9 (nine) would be 0 (zero).
As I recall (from 45 or so years ago), 0 (zero) is not actually a number, but a place-holder invented to separate positive numbers from negative numbers.
If you wrote 378 (3+7+8=18),then you could have either a zero or nine to add to the sum to make it a multiple of nine(18,27).
in other words your original number could have been 3078 or 3978. That why they told you not to circle zero so that you wouldn't have 2 numbers that could fit the answer.