Problem 009

[TheBonobo4]

0.23 seconds is quick, but can you get any quicker?

Level 1 is reached after 25 problems solved, then Level 2 at 50 and so on.

[Bee_Reay]

Haha! Probably not got time for that at the moment

[kicsishadow]

Hi!

I found an answer, where a + b + c = 1000, and a2+b2=c2 and a < b < c.

But if I type the solution in the format aaabbbccc, it says it is not correct. What could be the problem? Should I enter the solution in a different format?

[bruce_love]

Read carefully the last line of the question.

[kicsishadow]

I'm sorry, I'm from a non-English speaking country. For us, the sentence below

"Find the product abc"

means looking for the three numbers and then returning them side by side.

Using an example, if a is equal to 1200, b is equal to 2400, and c is equal to 3600, then the result I have to enter is: 120024003600.

Am I misunderstanding?

[hk]

the product abc is a*b*c. (multiply the three numbers)
If a=3 and b=4 and c=5 then abc=3*4*5=60.

[Liquid25677]

I don't understand the problem. It says there is only one triplet for which a+b+c=1000 but in fact you can find infinitely many using the formula for generating them:

Code: Select all

a = m^2 - n^2
b = 2mn
c = m^2 + n^2

m^2 - n^2 + 2mn + m^2 + n^2 = 1000

For example:
a = -1500 b = 800 c = 1700

Or:
a = -61500 b = 992 c = 61508

Is there something I'm missing? Should the numbers all be positive?

[mpiotte]

...
Is there something I'm missing? Should the numbers all be positive?

Yes, all numbers must be positive. It is implied by the general definition of Pythagorean triplet and natural numbers. Feel free to look them up.

[Liquid25677]

...
Is there something I'm missing? Should the numbers all be positive?

Yes, all numbers must be positive. It is implied by the general definition of Pythagorean triplet and natural numbers. Feel free to look them up.

OK, thanks. I thought that a Pythagorean triplet allowed negative numbers, but natural numbers are definitely always positive so I should nave read that more carefully.