, a, b, c, d, e, f are digits, a > 0

a is a digit and , so a can be 1 or 2. If a is 1, then x is 142857, if a is 2, x is 242857.

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- Nov 11th 2011, 09:33 AM #1

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## Problem

Find all 6-digit numbers

*x*with the following property:

If the first digit in x is deleted and added after the 5 other digits, you get a number that is 3 times as large as x.

For instance, the number x=158249 gets turned into 582491.

The number x=158249 does not meet the condition, because 3*158249 ≠ 582491

I hope that someone can help me with this problem - I have no idea how to solve it..

- Nov 11th 2011, 10:18 AM #2

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- Awetuouncsygg
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- Nov 11th 2011, 05:17 PM #3

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## Re: Problem

Hello, emilhp!

This can be solved as an Alphametic.

Find all 6-digit numbers*x*with the following property:

If the first digit in*x*is deleted and added after the 5 other digits,

you get a number that is 3 times as large as*x*.

We have: .

We see that:

If , the product will be a seven-digit number.

Suppose

We have: .

We have: .

We have: .

We have: .

We have: .

We have: .

Assume .and using similar reasoning,

. . we have: .