Math Trick

Here are the quick directions to follow.  If the directions are hard to follow then you can follow the example bellow.  It is possible somebody might not know what a sum is. 

Write down a number that is at least 5 digits long.  Subtract the sum of the digits.  Cross out a digit that is not a zero.  Send me the sum of the other digits.  I will be able to tell you what number you crossed out.

My Example:

Write down a number that is at least 5 digits long. 

99342

This number can be any number of digits long.  The longer it is the more interesting it is, but we want to keep the math simple too.

 Subtract the sum of the digits.  This means that we need to add up the digits and subtract that from the original.

9 + 9 + 3 + 4 + 2 = 27

To find the sum means to add them up.  In math the sum is the total.

99342 - 27 = 99315

We are subtracting the sum from the original number to get a new number.

Cross out a digit that is not a zero.

99315

The number in bold is the one that we will cross out for this example.

Find the sum of the other digits.

9 + 9 + 3 + 5 = 26

We find the sum of the other digits.

Send me the total.  In this particular example you would be sending me 26.  I should be able to tell you which number you crossed out.  If you send me 26 then I send you 1 which is the number that was crossed out in this example.  Sorry, I wouldn’t be able to tell you what your original number was since the final total is not enough information to determine that. 

This isn't a simple trick where you work backwards to figure out the theory behind it.  :)  If you can figure it out and be able to prove it then I would be impressed.  :)

I'm not sure if I'm getting this right.  I think so. 

I chose my own 5 digit number and ran it thought your algorithm described above.

My final sum was 9.

Now you tell me what number I crossed out.  Correct?

Awaiting your answer. 

Then I'll post my original number and the math steps, and confirm or deny your answer.

AquaMan wrote:

I'm not sure if I'm getting this right.  I think so. 

I chose my own 5 digit number and ran it thought your algorithm described above.

My final sum was 9.

Now you tell me what number I crossed out.  Correct?

Awaiting your answer. 

Then I'll post my original number and the math steps, and confirm or deny your answer.

 You must have crossed out a 9  :)

I crossed out a 0.

12345, sum of digits = 15.

12345 - 15 = 12330

crossing out 0, sum of digits = 9.

edit: did I screw it up?

haha, did I beat the algorithm with a corner case where the answer could be either 9 or 0?

AquaMan wrote:

I crossed out a 0.

12345, sum of digits = 15.

12345 - 15 = 12330

crossing out 0, sum of digits = 9.

edit: did I screw it up?

 Your math is correct.  :)  In the steps I provided it mentioned that you should cross out a digit that is not a zero.  :)

AquaMan wrote:

haha, did I beat the algorithm with a corner case where the answer could be either 9 or 0?

 You are correct.  :)

I'm sneaky :).  OK, I'll try another one.

My sum is 27.  What digit did I cross out?

edit:  oops, not sneaky, just careless.  Didn't follow the directions on the first one.

AquaMan wrote:

I'm sneaky :).  OK, I'll try another one.

My sum is 27.  What digit did I cross out?

edit:  oops, not sneaky, just careless.

 You crossed out a 9  :)

Correct!

10000

sum of digits = (thinking hard, um) 1

subtracting (thinking hard again, um) = 9999

crossing out... let's see... which number should I pick, um, 9

sum of remaining digits = 27

AquaMan wrote:

Correct. 

10000, sum of digits = (thinking hard, um) 1

subtracting (thinking hard again, um) = 9999

crussing out, let's see, which number should I pick?  OK, 9

sum of remaining digits = 27

 Very nice :)

My last example holds to PerfectGent's empirical solution.  I'm guessing he's right.

Google gave me one hit on exactly your directions, but no key to the trick and no proof :).  Scanned my discrete math books, no answer (my head hurts now, but only a little. I closed the books before it got too bad.)

Does anyone have the proof?  I don't want it yet though.

OK, I give.  Proof please.

Like many math tricks, this one relies on the rule of "casting out nines." When you subtract the sum of the digits from the original number, you always get a number that is divisible by 9. When a number is divisible by 9, its own digits always add up to be 9. Given the example, for instance, once the "seer" knows that the final derived number is 26, he knows that this is 1 less than the nearest number divisible by 9 (27), so he knows that a 1 must have been crossed out.

omg ... 2 complicated 4 me ... i wont even try it lol ...

but well done lol ... very interesting...

I love math tricks like these :)  The theory and proofs behind those are very complicated.

ok my number is 23

maniac2008 wrote:

ok my number is 23

 Then you crossed out a 4  :)