Number Logic

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Here’s one I got from an email. http://digicc.com/fido/%5B/url%5D. Can you figure out how it knows what you’ve circled? (It can be proven mathematically)

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Drew

I seem to have worked out the basics of the puzzle but not mathematics.

It appears to be pivot is factors of 9. If the total of the last numbers digit is say 7 the missing number would be 2, if the totals add up to say 11 the missing number is 7.

It seems to work but the reason to me is unclear

Jerry

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Yep, that’s the end result. What get’s you there, is the fact that we’re in base 10. So every digit is a power of 10. 1, 10,100,1000. Since the digits are the same, you always end up with a factor of nine in an equation. For example:

100x + 10y + z

if we rearrange it from xyz to yxz we get

100y + 10x +z

Subtract the two of those, and we get -90y + 90x, or 90(x-y). No matter what x or y (or z) is, the answer is divisible by 9. This works for as many digits as you want, because every factor of 10, subtracted from another, is going to result in a number divisible by 9. (or it will be zero (ie 10-10).

10-1=9
100-1=99
10000-100=9900
etc.

There is a rule in math, that a number divisible by 3, will also have the sum of it’s digits divisible by 3 also. That same rule applies to 9, therefore, as long as you are using the same digits, the difference will always have it’s digits total a multiple of 9.

Make sense?

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Yep, that’s the end result. What get’s you there, is the fact that we’re in base 10. So every digit is a power of 10. 1, 10,100,1000. Since the digits are the same, you always end up with a factor of nine in an equation. For example:

100x + 10y + z

if we rearrange it from xyz to yxz we get

100y + 10x +z

Subtract the two of those, and we get -90y + 90x, or 90(x-y). No matter what x or y (or z) is, the answer is divisible by 9. This works for as many digits as you want, because every factor of 10, subtracted from another, is going to result in a number divisible by 9. (or it will be zero (ie 10-10).

10-1=9
100-1=99
10000-100=9900
etc.

There is a rule in math, that a number divisible by 3, will also have the sum of it’s digits divisible by 3 also. That same rule applies to 9, therefore, as long as you are using the same digits, the difference will always have it’s digits total a multiple of 9.

Make sense?

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Drew

I seem to have worked out the basics of the puzzle but not mathematics.

It appears to be pivot is factors of 9. If the total of the last numbers digit is say 7 the missing number would be 2, if the totals add up to say 11 the missing number is 7.

It seems to work but the reason to me is unclear

Jerry

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