Problem 052

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abesto
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Joined: Sat Aug 02, 2008 10:41 am

Problem 052

Post by abesto »

Hi all, I just started solving the problems a few days ago, and I have to confess I'm having a great time :D
Two questions:
Problem 52 says "Find the smallest positive integer, x, such that 2x, 3x, 4x, 5x, and 6x, contain the same digits."
1. I guess (haven't solved this problem yet) that x, 2x, 3x, 4x, 5x, and 6x should contain the same digits. Is this correct?
2. The smallest positive integer that fits the criteria is 1, which is obviously not the expected answer... mby worth a note in the problem description?

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stijn263
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Re: Problem 52

Post by stijn263 »

1. This is correct
2. x = 1, means 2x = 2, and the integer 2 doesn't contain the same digits as 1. (313 fi contains the same digits as 331)

abesto
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Joined: Sat Aug 02, 2008 10:41 am

Re: Problem 52

Post by abesto »

Umm.. ermm... yeah. Kinda embarrassing, ain't it :D
Anyway, thanks for the answer

r-dog
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Joined: Sun Jun 28, 2009 1:53 am

Problem 052

Post by r-dog »

What is the interpretation:
1. "An x where 2x, 3x, 4x, 5x, 6x have same digits" ? (literal w/ no sample)
or,
2. "An x where 2x, 3x, 4x, 5x, 6x have same digits as x" ? (flexible w/ sample)

bassrael
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Joined: Sun Jul 12, 2009 11:49 pm

Re: Problem 052

Post by bassrael »

Saying 'as x' includes x having these digits, whereas the other phrase excludes x to have them.

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Georg
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Re: Problem 052

Post by Georg »

r-dog wrote:What is the interpretation:
1. "An x where 2x, 3x, 4x, 5x, 6x have same digits" ? (literal w/ no sample)
or,
2. "An x where 2x, 3x, 4x, 5x, 6x have same digits as x" ? (flexible w/ sample)
Do you get different results?

Vee
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Joined: Sun Oct 20, 2013 7:13 am

Problem 52

Post by Vee »

Hi all,

Problem 52 seems to have an incorrect definition.
It can be seen that the number, 125874, and its double, 251748, contain exactly the same digits, but in a different order.

Find the smallest positive integer, x, such that 2x, 3x, 4x, 5x, and 6x, contain the same digits.
I already found the 'correct' answer according to the euler-site, but in my opinion the answer to this question should be '1'. It is the smallest positive integer for which the values x2, x3, x4, x5 and x6 contain the same digits. Perhaps the question should be: Find the smallest positive integer greater than 1, x, such that ...

With kind regards,
Vee

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hk
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Re: Problem 52

Post by hk »

Does 2*1=2 have the same digit(s) as 1?
Image

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rayfil
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Re: Problem 52

Post by rayfil »

@Vee,

In this forum, problem numbers must have 3 digits, using leading 0`s for problem numbers below 100. You will notice that if you had done the proper search before making your post, you may have decided to the contrary.

Welcome to this forum.
When you assume something, you risk being wrong half the time.

Vee
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Joined: Sun Oct 20, 2013 7:13 am

Re: Problem 052

Post by Vee »

@rayfil: Thanks, I did use the search ("problem 52"), but now I know why no results came up.
And how wrong I was about multiples of 1 :)

Junglemath
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Re: Problem 052

Post by Junglemath »

The problem states: "Find the smallest positive integer, x, such that 2x, 3x, 4x, 5x, and 6x, contain the same digits."

I'm assuming that x itself also has the same digits as 2x, 3x, 4x, 5x, and 6x, but according to the wording of the problem this need not be the case. I don't see why there cannot exist a positive integer x such that 2x, 3x, 4x, 5x, and 6x have the same digits as each other but not the same digits as x.
Last edited by Junglemath on Mon Dec 09, 2019 8:28 pm, edited 1 time in total.

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hk
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Re: Problem 052

Post by hk »

The problem says nothing about x. It may have the same digits as 2x,3x,4x,5x and 6x or not. That's absolutely irrelevant.
Image

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