problem 206

[elendiastarman]

Problem 206 is slightly ambiguous.

Find the unique positive integer whose square has the form 1_2_3_4_5_6_7_8_9_0,
where each “_” is a single digit.

It didn't take me long to realize my mistake, but from the outset I assumed that all of the underscores were the same digit. Maybe it should be written this way:

Find the unique positive integer whose square has the form 1_2_3_4_5_6_7_8_9_0,
where each “_” is a single digit, not necessarily the same.

[hk]

If your interpretation was the one that was intended then you would have to take only 10 square roots to identify the answer wouldn't it?
Well these problems were meant as really easy, but that easy?
So quite little work to abolish that idea.
Let's try and do our best not "to search for nails on low water" too much.

[elendiastarman]

I suppose I was a little suspicious...

Also, at the time of this writing, 206 people have solved the 206^th problem!

[thekrazykid]

ok so i didnt think this was that hard but i got an answer that is definately right but im told it it is wrong.. 1013091779 squared is 1026354952677384900 which is in the form 1_2_3_4_5_6_7_8_9_0.. so how is this wrong?

[jaap]

How can an odd number squared be even?
1013091779² = 1026354952677384841

[thekrazykid]

hmm good point.. this doesnt make sence ive been playing around with my code and it gives me more than 1 square for the same number.. i thought this was just my code but google calculator does it too.. http://www.google.com/search?hl=en&q=10 ... h&aq=f&oq=http://www.google.com/search?hl=en&q=10 ... h&aq=f&oq=http://www.google.com/search?hl=en&q=10 ... h&aq=f&oq=
http://www.google.com/search?hl=en&q=10 ... h&aq=f&oq=

[jaap]

hmm good point.. this doesnt make sence ive been playing around with my code and it gives me more than 1 square for the same number.. i thought this was just my code but google calculator does it too..

It seems to gives more than one square root because it is getting rounded after nine or ten digits.
For example 1/3.

There is a limit on the value that a variable in a computer program can have. Most types use a fixed number of bytes of memory, so they don't hold necessarily hold as many digits as you might need.

[thekrazykid]

yea that was the problem.. i think google does it too because its coded it python and thats what im using.. im running it right now using a decimal module that will run it out farther

[MaJJ]

Hello,
I'm having a problem again
I have been solving #206 - and here's what I thought:

1_2_3_4_5_6_7_8_9_0 means that
- min = 1020304050607080900 (replacing _ with 0)
- max = 1929394959697989990 (replacing _ with 9)

And since both number and its square must be integers, let's calculate low = floor(sqrt(min)) and high = ceil(sqrt(max)).

Now I know that the answer lies somewhere between low and high.
So all I have to do is just square all integers in that range and eventually some of them will have the required form.

And my result - there isn't any! I went through all 378 925 614 ( ) of them and none of them has form 1_2_3_4_5_6_7_8_9_0 .
Where did I make a mistake?

[Tommy137]

Overflow bug?

[MaJJ]

I don't think so - I'm using Python, so this shouldn't happen. I'll try to check it though. Thanks

[Ted]

Maybe test with squares not square roots, as the latter may not resolve exactly to integers in some instances.

[MaJJ]

Hmm. But while working with square roots, I have to test only ~3.8 * 10^8 of them.
Once I'll start testing squares, I have to test ~ 10 times more numbers (if bruteforcing it in the way:

1020304050607080900
1020304050607080910
...
1020304050607080990
1020304050607081900
1020304050607081910
...

- adding 10 and when it jumps to another digit place, fixing it)

... as the latter may not resolve exactly to integers in some instances.

I don't get it. If answer to this problem has to be integer and integer^2 = another integer, my test with square roots should be correct. Or am I missing something?

EDIT: after this topic moved to another forum, I have read thekrazykid's issue - maybe there really is a overflow bug. But that's weird, Python lets me compute factorial of 10 000 and makes "simple" power function go wrong? I'm gonna try this "decimal" module ...

[daniel.is.fischer]

I would be very surprised if python got a simple power function wrong. If you don't find out yourself what went wrong, I'd be willing to take a look at your code.

[sdkudrgn88]

I got the right answer (at least I believe, it's verifiable with Windows Calculator), but Project Euler's site doesn't accept it as correct.

As it's not the "right" answer anyway, I don't think I'm doing any harm by posting it here:

The number is [...] (Alright, I think I know what I should do now. Thanks anyway.)

Am I doing something wrong, or is the number that "euler" found not unique...?

[JohnMorris]

I got the right answer (at least I believe, it's verifiable with Windows Calculator), but Project Euler's site doesn't accept it as correct.

As it's not the "right" answer anyway, I don't think I'm doing any harm by posting it here:

[...]

Am I doing something wrong, or is the number that "euler" found not unique...?

I'm not a Project Euler team member, but I'm guessing they would ask you to edit your mail to remove the numbers, unless they get there first. It would probably be appreciated if you did it.

Guessing: did you enter the square (1_2_3...) as your answer? The question asks for the number, not the square.

[sdkudrgn88]

I'm not a Project Euler team member, but I'm guessing they would ask you to edit your mail to remove the numbers, unless they get there first. It would probably be appreciated if you did it.

Guessing: did you enter the square (1_2_3...) as your answer? The question asks for the number, not the square.

As a matter of fact, that's exactly what I did. T_T...

[mdean]

Just got this one done. This one I cut a tad close. 47.33 seconds.

[quant42]

Because my algorithm to slove this problem don't return any answer - I want to know if I understand the problem correctly. We are searching x, such that the decimal representation of x * x matches the following regular expression: "1\d2\d3\d4\d5\d6\d7\d8\d9\d0"? (width \d short for [0-9])

[Marcus_Andrews]

quant42: That's correct.