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Cross out a number - any number - and I'll tell you what it


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5 replies to this topic

#1 bonanova

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Posted 31 August 2007 - 12:22 AM

I hand you a sheet of paper with the following instructions:

[1] Write down a 6-digit number. Say you write 352687
[2] Scramble the digits. Say you come up with 762853
[3] Subtract the smaller from the larger. You get: 762853 - 352687 = 410166
[4] Cross out one of the digits [but not a zero, cuz it's basically not there anyway.] Say you cross out a 6.
[5] Scramble the remaining digits. Say you get: 61401
[6] Tell me the digits. You say 6 1 4 0 1.

What are the odds that I will say, "you crossed out a 6"?
Spoiler for ...

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#2 bonanova

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Posted 31 August 2007 - 03:24 PM

Clue: How do the numbers 6 1 4 0 1 give away that 6 was crossed off?

Another case: 753487 - 345877 = 407610
this time cross out a 7.
scramble the remaining digits and tell me 6 0 0 1 4.

How do those numbers give away that a 7 was crossed off?
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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#3 normdeplume

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Posted 31 August 2007 - 04:21 PM

I don't have any mathematical proof, bt it appears fro the examples shown that all 6 digits of the result add up yo 18, so it is simple math 18- 12 in the first post and 18-11 in the second post.

Now Bananova can explain how / why we always come up with a digit total of 18, or is this just coincidence?
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#4 bonanova

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Posted 31 August 2007 - 05:35 PM

Now Bananova can explain how / why we always come up with a digit total of 18, or is this just coincidence?

You got it. Nice going!

And you resisted the red herring of 0 1 4 and 6 appearing in both cases.

The trick works because of two interesting properties of the number 9.

[1] scrambling a number's digits changes its value by a multiple of 9.
[2] adding the digits of a multiple of 9 gives another multiple of 9.

So the solution is to subtract the sum of the given digits from the next
higher multiple of 9. It just happened to be 18 both times here.

And the prohibition of not crossing out a zero is to distinguish
it from the case of crossing out a 9.

Now, can you prove these two interesting properties?
Spoiler for ...

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#5 unreality

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Posted 31 August 2007 - 09:31 PM

There are entire books- entirely scholarships- devoted to the number 9. It's my favorite number and i could probably load you up with so many "9-magic-tricks" and "9-riddles" it would make your brains explode! lol

but i'm content to sit back and watch other ppl solve em :D
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#6 smile4me

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Posted 01 September 2007 - 07:46 PM

pls post the riddles in separate threads
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