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OK, since I am a guru.(with a couple of math degrees)... I'll try this one

This trick challenges you to pick a four digit number and then scamble it. Subtract the smaller from the larger and then without knowing the two original numbers, you are asked to produce 3 of the 4 digits in the difference and somehow from that, the remaining digit of the difference can be ascertained

Example 3192 now scramble into 9132
Subtract the smaller 3192 from 9132 and you get 5940.
You are asked to provide any three digits from 5940 and miraculously the challenger can correctly guess the remaining one without knowing the random 3192 you started with or the random scramble of 3192 into 9132...

The trick is that regardless of what number you pick (and this works for 3,4,...digits), When you pick this number, scramble the digits and subtract the smaller from the larger, the difference will always have one property and that is that if you sum the digits in this difference it will always be a multiple of 9. Why.... It would take too long to go though that.. for now take my word and try it yourself.

Now lets call the Sum of the 3 digits provided sum3 and the missing number mnum

The formula to get the missing number is simply

mnum = 9 - (sum2 mod 9)

mod or modulo provides the remainder of one number divided by another.

Syntax
dividend mod divisor

Arguments
dividend
Is the numeric expression to divide. (A modulo is the integer that remains after two integers are divided.)

divisor
Is the numeric expression to divide the dividend by.

Getting back to our example, the difference between the two digits was 5940, whose sum of digits = 18

If I give the program 5, 9, 0 the sum or these three digits is 14 (sum3)

9 - (14 mod 9) =
9 - 5 = 4, the remaining digit.

The key trick in this brain teaser is that the resulting sum of digits for difference any number and any random scrambling of this number is always a number divisible by 9.

There the secret is now divulged... go impress your neighbors,

DB

Too bad your not LDAPguru, I might have some consulting for you.

gee I guess I got beat on the reply. but hey I'm no math major

I beg to differ from penzt8

4 digits don't always end up producing diferences whose sum of digits = 18

Example 8142-1284 = 6858 whose sum of digits = 27

What is true is that the sum of digits of difference between a number and a scramble of that number is always a multipl of 9

so if you get all but one of these digits,

the remaining one =

9 - ((sum of all but one of the digits) mod 9)

This will work for 3,4,5,6....any number of digits, even when one or more of the digits is zero and you scamble them any where, even to the leftmost position(s).

Guru, I am impressed. I was watching a show on the Curta hand calculator a couple weeks ago and it went into how Curta figured out how to do subtraction by adding 9's, or maybe it was multiplication, I dunno, but it had to do with the 9's thing, and made his invention possible. He figured it all out while he was in a Nazi concentration camp and used his abilities to keep himself and some others alive. It was fascinating and made me wish I had one of those marvelous mechanical calculators he invented. I think they go for about $1200 now. Quite a collectors item.

All I know is the 3,4,5 method to square of a roof to start your run row of shingles...

I can do figures and angels but nothing like guru.. pretty sharp!!!!

Hog

dbguru, you are correct.

I only ran two sets of numbers when I did this and they both totalled 18. I just made a quick assumption that was the case for all. I guess if I'd have done 2 or three more examples I might have come up with another multiple of 9. But who has that kind of time?