Nine Digits

baru...@arti.net.tr

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Apr 5, 1997, 3:00:00 AM4/5/97

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Here's one you perhaps know..

There is a 9-digit number in which the digits 1 through 9 appear exactly
once. If you only take the first n digits from left, the number you get
is divisible by n, (1<=n<=9). What is this unique number?

/\
|| Zafer Barutcuoglu - Bogazici University Dept. of Mathematics
\/
/\ "When all you have is a hammer, every problem looks like a nail."
\/

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baru...@arti.net.tr

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Apr 5, 1997, 3:00:00 AM4/5/97

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Here's one you perhaps know..

There is a 9-digit number in which the digits 1 through 9 appear exactly
once. If you only take the first n digits from left, the number you get
is divisible by n, (1<=n<=9). What is this unique number?

-------------------==== Posted via Deja News ====-----------------------

Brian MacBride

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Apr 5, 1997, 3:00:00 AM4/5/97

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baru...@arti.net.tr wrote in article <8602397...@dejanews.com>...

> Here's one you perhaps know..
>
> There is a 9-digit number in which the digits 1 through 9 appear exactly
> once. If you only take the first n digits from left, the number you get
> is divisible by n, (1<=n<=9). What is this unique number?
>

> /\
> || Zafer Barutcuoglu - Bogazici University Dept. of Mathematics
> \/
> /\ "When all you have is a hammer, every problem looks like a nail."
> \/
>

> -------------------==== Posted via Deja News ====-----------------------
> http://www.dejanews.com/ Search, Read, Post to Usenet
>

[SPOILER]

The number is....

381654729

Regards
Brian

Steve Cox

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Apr 5, 1997, 3:00:00 AM4/5/97

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baru...@arti.net.tr wrote:
>
> Here's one you perhaps know..
>
> There is a 9-digit number in which the digits 1 through 9 appear exactly
> once. If you only take the first n digits from left, the number you get
> is divisible by n, (1<=n<=9). What is this unique number?

SPOILER

381654729

Let the number be abcdefghi

Since there are no zeros, e is 5.
b,d,f, and h must be even, a,c,e,g, and i odd.
Any multiple of four has as its last two digits a multiple of four.
So cd must be in {12,16,32,36,72,76,92,96}
So d is 2 or 6.
Any multiple of 8 has as its last three digits a multiple of eight.
So fgh must be in {216,232,272,296,416,432,472,496,616,632,672,
696,816,832,872,896}
So h is 2 or 6.
Since abc is a multiple of 3, def is also.
Of the possibilities def {2,6}{5}{4,8} only 258 and 654 are
divisible by 3.
If def is 258, the number is a4c258g6i, where g is 1 or 9 (from fgh)
abc possibilities are 147 and 741, with g being 9
neither 1472589 nor 7412489 are divisible by 7
So def must be 654, the number is a8c654g2i, where g is
3 or 7 (from fgh)
abc must be in {183,189,381,789,981,987}
Calculation shows only 3816547 is divisible by 7. i is 9, so
the number is 381654729.

-Steve Cox

Snibor Eoj

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Apr 6, 1997, 4:00:00 AM4/6/97

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Here's a solution... I haven't checked its uniqueness, but I think it
probably is unique.

381654729

Snibor Eoj

jmro...@sccs.swarthmore.edu http://www.cs.swarthmore.edu/~robins/
------------------------------------------------------------------------------
I'm a member of the Non-Sequitur Association of America
A fish said to two translucent dogs:
"A marble flower is too delicious for the morning sacrifice.
Linger here no longer."
And then it died.

Soh Chin Ann

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Apr 7, 1997, 3:00:00 AM4/7/97

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Snibor Eoj wrote:
>
> Here's a solution... I haven't checked its uniqueness, but I think it
> probably is unique.
>
> 381654729
>
> Snibor Eoj

This solution is unique, I checked already.

Chin Ann