- #1
AlfieD
- 68
- 0
A door company makes doors out of square wooden panels. After installing many doors, they are asked to install a security cable that runs diagonally from the top right to the bottom left. With an n*m door, how many panels need to be lifted to place the security cable?
So what I did at first was just draw out some basic representations to see if any patterns jumped out at me: I did 5x4 and got 7 panels, 4x6 got me 8 panels, 4x7 got me 9, 5x6 got me 10, 5x7 got me 11, and 6x7 got me 12. So I started thinking if it was n+m-1, etcetera, but to no avail. I could see a pattern, but not a pattern for every one (there were groups where a pattern worked); I couldn't find a formula that was consistent, no matter what n or m equalled.
If someone could shed some light on this I would be appreciative. I don't actually know if there is an answer, but there probably is because I doubt I'd be set such a tedious homework!
Thanks in advance,
AlfieD
So what I did at first was just draw out some basic representations to see if any patterns jumped out at me: I did 5x4 and got 7 panels, 4x6 got me 8 panels, 4x7 got me 9, 5x6 got me 10, 5x7 got me 11, and 6x7 got me 12. So I started thinking if it was n+m-1, etcetera, but to no avail. I could see a pattern, but not a pattern for every one (there were groups where a pattern worked); I couldn't find a formula that was consistent, no matter what n or m equalled.
If someone could shed some light on this I would be appreciative. I don't actually know if there is an answer, but there probably is because I doubt I'd be set such a tedious homework!
Thanks in advance,
AlfieD