problem 206

[Oliver1978]

So, I gather from the previous posts that those "_" digits do not have to be distinct?

[Marcus_Andrews]

Right -- they do not have to be distinct.

[Oliver1978]

Danke, Marcus. Solved it then.

[thechosenone98]

Hi, I am posting this as a suggestion to verify that there is in fact only 1 possible positive
number that, once squared, gives another number in the form :
1_2_3_4_5_6_7_8_9_0 (where _ is a single digit)

EDIT: Each _ can be any single digit and they can be repeated.

While i was giving it a go with my calculator and a bit of brainage I found that
the number 1 388 659 302 squared gives the number : 1928374655647382910
which to my understanding also respects the form given above
(Note that the square shown above is just the sequence 987654321 imbeded in the form given by the problem (that is the sequence 123456789 reversed and splitted appart in each _ places.
I, in fact, found this number by taking the square root of 1928374655647382910 (It just seemed so perfect it had to work you know ).

So please correct me if I'm wrong or modify the problem 206 so that it asks you for the sum of every possible combination if and only if my answer is right too of course

As of right now, the only accepted answer is <value removed by moderator> <-- Oh well...

Have a nice day

[RobertStanforth]

@thechosenone98:
I have moved your post to the correct forum for problem clarifications.

Also, please do not post answers in public view!!! I have removed it from your post.

To answer your question, 1388659302 is not a valid solution. The value you give for its square is not correct, and is not even a square. The problem does indeed have only one answer.

[thechosenone98]

I don't get what you mean by it is not even a square. You have to square it to get my answer. Isn't that what the question wants (a number whose square is of the form 1_2_3_4_5_6_7_8_9_0)?

[RobertStanforth]

1928374655647382910 is not a perfect square.

[thechosenone98]

Well according to my calculator it is. I'm very confused right now To test if it is a perfect square I just take the square root of it and if it gives me an integer it is then a perfect square right?

[thechosenone98]

Very sorry about that (i tried to take the square root in python and you are in fact correct). I just found the limitation of this amazing calculator lolz.

[RobertStanforth]

I expect your calculator is rounding to ten significant digits, so the fractional part has been truncated.

[DJohn]

You don't need a calculator to see that you've gone wrong: The last digit of 1388659302 is 2. Whatever the square is, its last digit will be 4, not 0.

[thechosenone98]

Yes i can actually find the fractinnal part if I substract the whole integer part from it and than it gives me the fractionnal reminder part...It is sad that it doesn't show me that there is a fractionnal part even if it doesn't have any more space on screen to display it (there should be an indicator or something, that would be nice).

[thechosenone98]

Anyway thanks for your time buddy I appreciate it

[dawghaus4]

...
While i was giving it a go with my calculator and a bit of brainage I found that
the number 1 388 659 302 squared gives the number : 1928374655647382910
which to my understanding also respects the form given above
...

The square of any number ending in 2 will end in 4.

The square root of any number ending in 0 will end in 0.

Tom