Problem 052

[abesto]

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]

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]

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

[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]

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

[Georg]

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]

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]

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

[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.

[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]

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.

[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.