How does this crazy mind reading online puzzle work? Is there some kind of math formula or something?

Question

http://digicc.com/fido/

I can't figure out how this works... Anyone know the trick? Its driving me crazy! ^_^

http://digicc.com/fido/

OK, in response to the first comment, NO i'm not trying to advertise anything. Actually, i drink Dr. Pepper. I really don't like mountain dew. The truth is, I'm a freshman in college and I need to know the answer for a Problem Solving class at the University of Alabama.

Answer 1

You can prove this algebraically. Let's let the bigger number be 'abc'. This breaks down to:
100a + 10b + c

The reversed number is 'cba'. This becomes:
100c + 10b + a

When you subtract, the 10b terms cancel out and you get:
99a - 99c

Since 'a' is greater than 'c' (and all digits are different), this will be a positive number. (If a and c were the same, you would end up with zero. But this is why they tell you to pick a "completely random number with all the digits different".)

You can factor out a 9:
9(11a - 11c)

So this proves that no matter what 3 digit number you pick, the result will be a multiple of 9.

The same is true for a 4 digit number 'abcd':
1000a + 100b + 10c + d
The reverse is 'dcba'
1000d + 100c + 10b + a

Subtracting:
999a + 90b - 90c - 999c

Again you can factor out a 9:
9(111a + 10b - 10c -111c)

You could actually do this with 2 digit numbers, 5 digit numbers, 6 digit numbers, etc. With 2 digit numbers, you are liable to end up with only a single digit (9), so that wouldn't be too exciting and the trick might be apparent. With more digits, you are likely to make a subtraction error and ruin the trick. So they settled on 3 or 4 digits.

As we learned in school, the digits of a multiple of 9 also add up to a multiple of 9.

So when you leave out a digit, the program can easily figure out what number is missing to make it add up to a multiple 9. For example, 1089...

If I tell the program everything but 1, the remaining digits (0,8,9) add up to 17... the next multiple of 9 is 18. The difference is 1.
Or if I pick 8, the remaining digits (1,0,9) add up to 10. The next multiple is 18 and the difference is 8.
If I pick 9, the remaining digits (1,0,8) add up to 9. The *next* multiple of 9 is 18, so the difference is 9.

Now notice they told you *not* to circle a zero (giving some excuse like "it is already a circle"). The reason they did this is that subtracting 0 or 9 will always make another multiple of 9, and it wouldn't be clear if the number that was removed was a 0 or 9. If they disallow you from picking a zero, this ambiguity goes away. Thus the program always looks for the digit that will get to the next multiple of 9.

I hope I've saved your sanity now that you know the math formula and all the tricks.

Answer 2

Oh, I get it now! The result you get from the subtraction will always equal a number that's sum of its digits is divisible by 9 (normally 18). Then when you type in the number you have left, it displays the digit needed to create said sum, which is convieniently the number you crossed out. Example:

4321-1234= 3087
3+8+7=18
you cant cross out 0 so lets say you cross out 3
whatever you put in, the computer sees 8+7+?=18

(it knows the result is either 27, 18 or 9 because the number you put in has 3 digits, and those are the only multiples of three that can be made with three digits and seeing as 8+7 cant equal 9 or 27 without using negative numbers or numbers >9, it assumes 8+7+?=18)

the only combination of 8+7+?=18 is 8+7+3, so naturally you crossed out 3.

There you have it. It's a simple calculating program that you could use on friends. If this explanation is too complicated, sorry. If not, BEST ANSWER!

PS: This question does not count as spam because I'd like to see someone explain this as a question without usage of the link.

Answer 3

The key lies in a characteristic of the number 9. If you transpose the digits in a number and subtract the smaller number from the larger, the difference is always evenly divisible by 9.

http://britton.disted.camosun.bc.ca/jbfido.htm explains it all

Answer 4

Stupid Fido puzzle. It's been around since like the early 1800's and Mtn dew thinks they are coming up with somthing new. Ridiculous! Ya that guy above me pretty much hit it on the head why it works.

Answer 5

The only thing is if you pick 123 and scramble it to 321...it doesn't work...

And none of my differences were divisible by nine...so it has nothing to do with inverse numbers.

Answer 6

trying to do some micro-marketing for Seven Up, are we?

why don't you let non-commercial people play here