Word Problems guide 5 (Page 140, Q 8)

[syeda.q.masood]

Hello
I do not understand the logic used to answer this question. Can you please elaborate on what is already given in the guide? "The least possible length of the longest piece" is confusing.
Thanks
S

[tommywallach]

Hey Syeda,

Unfortunately, I've looked over that explanation, and it's really good. I'm not sure there's a better way to explain it. But I can try, I suppose.

"The least possible length of the longest piece" means that we want to know the smallest we can make the piece of the ribbon that will be the biggest one.

For example, the longest piece can't be one inch, because the other two pieces would need to be smaller, which isn't possible.

The longest piece can't even be five inches, because the other two would be four inches and three inches, and they wouldn't add up to 40.

So we're trying to find what the LEAST that longest piece can be is.

If the longest piece were 14 inches, the other two could be 13 and 12, and they'd all add up to 39 inches, so we still wouldn't get to 40 inches. So the shortest that the longest piece can be is 15 inches.

Hope that's better! : )

-t