Ok, this is freaky.

It freaked me out, too, especially with that menacing music.

I found out how it works, though I don't think I would have ever figured it out myself.

Steven

0,9,18,27,36,45 etc. are all multiples of 9. They all have the same symbols. The answers are always multiples of 9.

They change the symbols for each trial, but they are still the same numbers.

To explain why they always end up with multiples of nine, using algebra:
Let the number for example be 52.
Let x=5
Let y=2
Then the number is 10x + y.
You are asked to add the digits.
That's x+y.
Then substract that from the original number.
That's 10x + y minus x minus y
Result is 9x which is a multiple of 9.
Try any number. The result is always a multiple of 9.

so how do they gee the correct symbol then?

In any one trial, your answer will always be a multiple of 9. All multiples of 9 always have the same symbol in any one trial. Therefore, in any trial the gopher just says what that symbol is and he'll be right. In the next trial, the gopher says what the symbol allocated to all multiples of 9 that time is, and he'll be right again, because once again your answer will always be a multiple of 9.

Unless you're lousy at math. Then the gopher gets it wrong.

So that's how I managed to fool the gopher! I knew being lousy at maths must have some advantages!

Is there any way to actually not get a multiple of 9??

Sloppy math.

sorry cananot help
I'm not good enough

Make up a number, with any number of digits, rearrange the digits (anagram them), subtract one from the other, and the answer will always be a multiple of 9. There are a number of "parlor" tricks that use this phenomenon.

e.g.:

74526984 minus 28465794 = 46061190

Sum the digits in the answer: 4+6+0+6+1+1+9+0 = 27
Sum those digits: 2+7=9

I'll leave the proof to somebody else!

I couldn't resist: Here is an explanation/sketch of proof ( a formal proof would require notation that is more difficult to type out, along with some special cases)

Example: Original number 24971, new number 17249. The difference is 7722 whose sum of digits is 18.

7722 also equals (2-1)*10000+ (4-7)*1000 +(9-2)*100 +(7-4)*10 +(1-9)*1.

The sum of digits = (2-1) +[-1+10-(-(4-7))] + (9-2)+(7-4)+[-1+10-(-(1-9))]
= 2*9 + [(2-1) + (4-7) +(9-2)+(7-4)+(1-9)]
= 2*9 +(2+4+9+7+1) -(1+7+2+4+9)= 2*9 +0

In the first line of the sum of digits expression, the negative expressions in red contributes to the sum of digits in a different way than each positive expression. Essentially that is because to subtract a number from say the thousandth place, you subtact 1 from the ten-thousandth place and then take 10 - your number, the normal way subtraction is done. The next part of a proof relies on the fact that a permutation of the digits of the original number does not change the sum of the digits, that is, the sum of digits in 24971 and 17249 is the same, hence the expression in blue is 0.

Since the difference between the original number and the new number is always a multiple of 9, and that any multiple of 9 always has sum of digits 9, the sum of digits of the difference is always 9.

hey i can't open it. please suggest me how can see it?