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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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Apr 5, 1997, 3:00:00 AM4/5/97

to

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 ====-----------------------

Apr 5, 1997, 3:00:00 AM4/5/97

to

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

Apr 5, 1997, 3:00:00 AM4/5/97

to

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?

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

Apr 6, 1997, 4:00:00 AM4/6/97

to

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.

Apr 7, 1997, 3:00:00 AM4/7/97

to

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

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