Tuesday Puzzle

9/30/08, 11:42 AM #1

Dan Donaldson
Member
Offline
5,264 posts

Registered: 9/17/01

Tuesday Puzzle

Two ladders are placed cross-wise in an alley to form a lopsided X-shape. The walls of the alley are not quite vertical, but are parallel to each other. The ground is flat and horizontal. The bottom of each ladder is placed against the opposite wall. The top of the longer ladder touches the alley wall 5 feet vertically higher than the top of the shorter ladder touches the opposite wall, which in turn is 4 feet vertically higher than the intersection of the two ladders. How high vertically above the ground is that intersection?

A sketch is attached.

(Alex, wait for at least a little bit before you answer and give others a bit of a chance ;-)) YOu are way good at these ;-)

- - -

I have been woodworking for about 25 years now, and would consider myself an enthusiastic amateur. My claim to fame (or infamy) has always been fixing stuff. I spent time in the Air Force in the 60's then went to work as an electronic technician for civil service. I finally got my EE, and being fed up with the civil service nonsense, took a job with Ford Motor Company until I went with the split to Visteon last year. I got interested in music and started playing in a bluegrass band. I wanted a new guitar, and that kind of led me into woodworking. I bought some books, a few tools, and built a guitar. Luckily, I didn't know any better than to try that as a first ever project. I still play it when I get a chance, so it must not be too bad if it can live for over 20 years. After a stint in Mexico for my job, I moved into a new house and built a small shop. Since then I have been collecting tools and skills, probably more of the former than the latter ;-). Finding this site has done more for my skills and enjoyment than anything else. I have learned a lot and really enjoy the friendships that I have made here. I have been married to LOML (Lori) for 32 years now and have 6 kids. When they are all gone, I want to get a 1 bedroom house (so there is not room for them to move back in) and at least a 6 car heated/air conditioned garage for a shop. (Dream on...)

Re: Tuesday Puzzle

9/30/08, 2:37 PM #2

Thomas Skaggs
Guest

Re: Tuesday Puzzle

Are they wooden ladders or aluminum?

Re: Tuesday Puzzle

9/30/08, 2:59 PM #3

Dan Donaldson
Member
Offline
5,264 posts

Registered: 9/17/01

Re: Tuesday Puzzle

They are made of unobtanium ;-)

- - -

I have been woodworking for about 25 years now, and would consider myself an enthusiastic amateur. My claim to fame (or infamy) has always been fixing stuff. I spent time in the Air Force in the 60's then went to work as an electronic technician for civil service. I finally got my EE, and being fed up with the civil service nonsense, took a job with Ford Motor Company until I went with the split to Visteon last year. I got interested in music and started playing in a bluegrass band. I wanted a new guitar, and that kind of led me into woodworking. I bought some books, a few tools, and built a guitar. Luckily, I didn't know any better than to try that as a first ever project. I still play it when I get a chance, so it must not be too bad if it can live for over 20 years. After a stint in Mexico for my job, I moved into a new house and built a small shop. Since then I have been collecting tools and skills, probably more of the former than the latter ;-). Finding this site has done more for my skills and enjoyment than anything else. I have learned a lot and really enjoy the friendships that I have made here. I have been married to LOML (Lori) for 32 years now and have 6 kids. When they are all gone, I want to get a 1 bedroom house (so there is not room for them to move back in) and at least a 6 car heated/air conditioned garage for a shop. (Dream on...)

Re: Tuesday Puzzle

9/30/08, 3:20 PM #4

Ed in Leaside
Member
Offline
234 posts

Registered: 11/3/05

Re: Tuesday Puzzle

Is it twice the short side of the Greek guy's triangle?

Re: Tuesday Puzzle

9/30/08, 4:48 PM #5

Dan Donaldson
Member
Offline
5,264 posts

Registered: 9/17/01

Re: Tuesday Puzzle

Depends on which one you are referring to. ;-) That is correct if the smallest one.

- - -

I have been woodworking for about 25 years now, and would consider myself an enthusiastic amateur. My claim to fame (or infamy) has always been fixing stuff. I spent time in the Air Force in the 60's then went to work as an electronic technician for civil service. I finally got my EE, and being fed up with the civil service nonsense, took a job with Ford Motor Company until I went with the split to Visteon last year. I got interested in music and started playing in a bluegrass band. I wanted a new guitar, and that kind of led me into woodworking. I bought some books, a few tools, and built a guitar. Luckily, I didn't know any better than to try that as a first ever project. I still play it when I get a chance, so it must not be too bad if it can live for over 20 years. After a stint in Mexico for my job, I moved into a new house and built a small shop. Since then I have been collecting tools and skills, probably more of the former than the latter ;-). Finding this site has done more for my skills and enjoyment than anything else. I have learned a lot and really enjoy the friendships that I have made here. I have been married to LOML (Lori) for 32 years now and have 6 kids. When they are all gone, I want to get a 1 bedroom house (so there is not room for them to move back in) and at least a 6 car heated/air conditioned garage for a shop. (Dream on...)

Re: Tuesday Puzzle

9/30/08, 5:01 PM #6

Dan Donaldson
Member
Offline
5,264 posts

Registered: 9/17/01

BTW

Just in case someone else is wondering, the 3-4-5 is the most commonly known (along with any multiples thereof), but there are several other perfect triples, namely 5-12-13, 7-24-25, 8-15-17, and 9-40-41 (and their multiples). When I have had kids start working with right triangles, I encourage them to memorize these because on most standardized tests, the problems will almost certainly be one of these (because they are nice round numbers) and you can save yourself a lot of time if you recognize them. (Useless piece of misc. information ) ;-)

- - -

I have been woodworking for about 25 years now, and would consider myself an enthusiastic amateur. My claim to fame (or infamy) has always been fixing stuff. I spent time in the Air Force in the 60's then went to work as an electronic technician for civil service. I finally got my EE, and being fed up with the civil service nonsense, took a job with Ford Motor Company until I went with the split to Visteon last year. I got interested in music and started playing in a bluegrass band. I wanted a new guitar, and that kind of led me into woodworking. I bought some books, a few tools, and built a guitar. Luckily, I didn't know any better than to try that as a first ever project. I still play it when I get a chance, so it must not be too bad if it can live for over 20 years. After a stint in Mexico for my job, I moved into a new house and built a small shop. Since then I have been collecting tools and skills, probably more of the former than the latter ;-). Finding this site has done more for my skills and enjoyment than anything else. I have learned a lot and really enjoy the friendships that I have made here. I have been married to LOML (Lori) for 32 years now and have 6 kids. When they are all gone, I want to get a 1 bedroom house (so there is not room for them to move back in) and at least a 6 car heated/air conditioned garage for a shop. (Dream on...)

Re: Tuesday Puzzle

10/1/08, 1:30 AM #7

Ed in Leaside
Member
Offline
234 posts

Registered: 11/3/05

Yes, 3-4-5

Re: Tuesday Puzzle

10/1/08, 2:24 AM #8

Alex Yeilding
Guest

Stumped

Your request was not needed!!

I think the key is adding some more triangles, then working with similar and equivalent triangles, but I'm at a loss.

What's particularly frustrating is that I have seen another very similar puzzle, which also stumps me. I wouldn't be surprised to find them in some sense mathematically equivalent. I'll try to remember to post that next week.

I'll pull a few more hairs out, then check back here.

Re: Tuesday Puzzle

10/1/08, 2:51 AM #9

Jerry Glaser
Guest

Re: Stumped

six and a half feet

Re: Tuesday Puzzle

10/1/08, 3:02 AM #10

Dan Donaldson
Member
Offline
5,264 posts

Registered: 9/17/01

Re: Stumped

Consider the following sequence of diagrams. In each, like-colored triangles are similar. This follows because the alley walls are parallel.

By similar triangles, 9/h = h/4.

Hence h2 = 36.

Rejecting the negative root, h, the vertical height of the intersection above the ground, is 6 feet.

- - -

I have been woodworking for about 25 years now, and would consider myself an enthusiastic amateur. My claim to fame (or infamy) has always been fixing stuff. I spent time in the Air Force in the 60's then went to work as an electronic technician for civil service. I finally got my EE, and being fed up with the civil service nonsense, took a job with Ford Motor Company until I went with the split to Visteon last year. I got interested in music and started playing in a bluegrass band. I wanted a new guitar, and that kind of led me into woodworking. I bought some books, a few tools, and built a guitar. Luckily, I didn't know any better than to try that as a first ever project. I still play it when I get a chance, so it must not be too bad if it can live for over 20 years. After a stint in Mexico for my job, I moved into a new house and built a small shop. Since then I have been collecting tools and skills, probably more of the former than the latter ;-). Finding this site has done more for my skills and enjoyment than anything else. I have learned a lot and really enjoy the friendships that I have made here. I have been married to LOML (Lori) for 32 years now and have 6 kids. When they are all gone, I want to get a 1 bedroom house (so there is not room for them to move back in) and at least a 6 car heated/air conditioned garage for a shop. (Dream on...)

Re: Tuesday Puzzle

10/1/08, 5:39 AM #11

Alex Yeilding
Guest

Re: Stumped

Just signed back on to post that answer! Clever distraction talking about 3-4-5 right triangles. I wasted lots of time on that false lead! ;-)

Re: Tuesday Puzzle

10/1/08, 12:05 PM #12

Dan Donaldson
Member
Offline
5,264 posts

Registered: 9/17/01

Re: Stumped

Traditionally, one of the goals on the trivia board is to keep the threads going as long as possible. Creative answers are encouraged, and bonus points given for really creative ones even if they actually have nothing to do with a correct answer. It is all in fun. ;-)

- - -

I have been woodworking for about 25 years now, and would consider myself an enthusiastic amateur. My claim to fame (or infamy) has always been fixing stuff. I spent time in the Air Force in the 60's then went to work as an electronic technician for civil service. I finally got my EE, and being fed up with the civil service nonsense, took a job with Ford Motor Company until I went with the split to Visteon last year. I got interested in music and started playing in a bluegrass band. I wanted a new guitar, and that kind of led me into woodworking. I bought some books, a few tools, and built a guitar. Luckily, I didn't know any better than to try that as a first ever project. I still play it when I get a chance, so it must not be too bad if it can live for over 20 years. After a stint in Mexico for my job, I moved into a new house and built a small shop. Since then I have been collecting tools and skills, probably more of the former than the latter ;-). Finding this site has done more for my skills and enjoyment than anything else. I have learned a lot and really enjoy the friendships that I have made here. I have been married to LOML (Lori) for 32 years now and have 6 kids. When they are all gone, I want to get a 1 bedroom house (so there is not room for them to move back in) and at least a 6 car heated/air conditioned garage for a shop. (Dream on...)

Re: Tuesday Puzzle

10/1/08, 2:14 PM #13

Don Orr
Member
Offline
3,243 posts

Registered: 1/2/04

Re: Stumped

Hey is that THE Jerry Glaser of awesome turning tool fame ? If it is he sure knows a lot about useful angles ! Especially on cutting edges applied to rapidly rotating wood.

- - -

My name is Don and I'm a Turning addict. There, I finally can admit I have a problem. The problem is not enough time to turn! I work as a Medical Imaging Tech for a living but that's just so I can light and heat the shop and buy more tools. I've been turning since 2000 and it has changed my life. I never had a creative outlet before I discoverd Woodturning and now I can't get enough. After I turned my first pen, my wonderful wife saw how excited I was and bought me a mini lathe. She now refers to herself as a "Turning Widow". She is a potter and quilter so she understands the obsession. My interests in turning are many and varied and I'm sure I will not live long enough to try everything I'd like to, but I'll give it a shot. Unfortunately we don't have any children or pets so you'd think I have all kinds of free time to turn, but for some reason I don't. I belong to the Adirondack Woodturners Association in upstate New York, the Mohawk Valley Woodturners, the Old Country Guild of Woodturnes and AAW, as well as the Northeastern Woodworkers Association. (I'd also like to learn to do flatwork someday.) Happy and Safe Turning, Don

Tuesday Puzzle

Posts