## Problem 052

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abesto
Posts: 2
Joined: Sat Aug 02, 2008 10:41 am

### Problem 052

Hi all, I just started solving the problems a few days ago, and I have to confess I'm having a great time
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?

stijn263
Posts: 1505
Joined: Sat Sep 15, 2007 10:57 pm
Location: Netherlands

### Re: Problem 52

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
Posts: 2
Joined: Sat Aug 02, 2008 10:41 am

### Re: Problem 52

Umm.. ermm... yeah. Kinda embarrassing, ain't it

r-dog
Posts: 5
Joined: Sun Jun 28, 2009 1:53 am

### Problem 052

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
Posts: 2
Joined: Sun Jul 12, 2009 11:49 pm

### Re: Problem 052

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

Georg
Posts: 157
Joined: Mon Jan 21, 2008 7:00 am
Location: Mannheim, Germany
Contact:

### Re: Problem 052

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
Posts: 2
Joined: Sun Oct 20, 2013 7:13 am

### Problem 52

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

hk
Posts: 10659
Joined: Sun Mar 26, 2006 9:34 am
Location: Haren, Netherlands

### Re: Problem 52

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

rayfil
Posts: 1403
Joined: Sun Mar 26, 2006 4:30 am
Contact:

### Re: Problem 52

@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
Posts: 2
Joined: Sun Oct 20, 2013 7:13 am

### Re: Problem 052

@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
Posts: 27
Joined: Fri Sep 20, 2019 12:25 pm

### Re: Problem 052

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.

hk