NeoPets Riddles (Lenny Conundrums) and Answers Here

-sigh- this would be so much easier if 399994 was a square number!

hm...is 480160 somewhat close to the answer?

****THE ANSWER IS 707^2 = 499849****
There is no "formula" for solving a problem like this. You have to use intelligent guess-n-check, and work your way through the options.

If the sum of the six digits is forty-three, then average digit is a seven. So the number could be pretty danged large, and not many of the digits in the number can be very small.

If the number is a cube, then it can be no more than 99^3 = 970 299 and no less than 47^3 = 103 823.

If the number is a square, then it can be no less than 317^2 = 100 498 and no more than 999^2 = 998 001.

You can use an Excel spreadsheet to do any amount of the computations that you like. (It's just a matter of how much programming you want to do.) It is fairly simple to do one column with the starting value (from above) and the next column as the square or cube of that value. Extend the table down until you've reached the maximum value. Then eyeball the numbers in the square or cube column. Most of them will be easily discarded, because their digits are not sufficiently large, or not enough of them are sufficiently large. Only bother to sum the digits of the other ones.

I didn't find any cubes that worked. But when I did a squareds table, I found the following:

******************************
******** 707^2 = 499849 ********
**** 4 + 9 + 9 + 8 + 4 + 9 = 43 ****
******************************

Eliz.

Has anyone figured it out yet?

Umm, maybe see the post before yours.

lmao.... look above your post 007, you may find at least one who has solved it

I got it!

oooh, someone else did before me...oh well

The neoboards are talking about there being more than one answer. I'd like to see how TNT handles that.

haha, how can there be more than one?

yay!! wow, dat's quick for such a confusing prob... @_@

Interesting observation. There is no single cube number that is between 1^3 and 65000^3 (this is as far as excel will go in one shot) whose sum of digits is 43.

Therefore it must be square and under 500000, which leaves 499849 as the only answer between 1 and 65000^3. It would be an interesting problem to *prove* that no cube number can have a sum of digits of 43, but it goes beyond the scope of this problem, since we have a single answer that fits the question. I'm pretty sure TNT meant that one...

Yeah, reading through the other posts, I'm thinking people only said that to throw off those begging for the answer. I don't mind when people ask for the answer there, personally, because it DOES get posted here.

It's the whiners that bother me.

There is a simple proof that there is no cube with digits that sum to 43. The digital root of N cubed is the cube of the digital root of N. No cube has a digital root of seven (you only have to test the numbers 0-8 to show this); so no cube can have digits that sum to 43.

Also, only numbers with digital roots of four or five have squares with digital roots of seven. Therefore, for this problem, you only have to check 2/9 of the squares in the range that stapel provided.

The digital root of a number, N, is N mod 9 (the remainder when you divide N by 9). It can be computed by adding the digits of N. If the sum has more than one digit, repeat the process on the sum. Continue until you get to a single digit (0 and 9 are equivalent). It's also called casting out the nines.

Answers
As of now I I have come across two answers that seemingly work. I assume that TNT will accept both or any answer that applies to the requirements of the riddle. They can't exactly accept only one answer.

Um i feel kinda stupid I dont know the answer do you ?

Oy. Here we go again....

As was posted on the previous page:

******************************
***** HERE IS THE ANSWER: ******
******************************
******** 707^2 = 499849 ********
******************************
**** 4 + 9 + 9 + 8 + 4 + 9 = 43 ****
******************************

Please let me know if you're still having trouble finding the answer.

Eliz.

Re: Answers

They sure can because there is only one answer. What two numbers do you think are valid solutions?

Ok so it is just 499849 thanx

so what numbers do you type in, in the answer box?

Is it 43 or
499849?

Sorry im getting all confused