Friday puzzle -- The Cadets' Mascot

8/1/09, 3:39 AM #1

Alex Yeilding
Guest

Friday puzzle -- The Cadets' Mascot

Sorry I'm late with this one.

A square formation of army cadets, 50' on a side, is marching at a constant pace, parallel to two sides of the square. Their mascot, a small terrier, starts the the back rank, and runs forward (at a constant pace) to the front rank of cadets, where it instantaneously reverses direction and runs back to the back rank (at the same pace). It reaches the back rank exactly where the front rank was when the terrier started running toward the front rank (i.e., the formation of cadets has marched 50').

How far has the dog run?

Re: Friday puzzle -- The Cadets' Mascot

8/1/09, 12:13 PM #2

Dan Donaldson
Member
Offline
5,264 posts

Registered: 9/17/01

Re: Friday puzzle -- The Cadets' Mascot

I took the % phase of the moon, added the number of seeds on an acacia, multiplied by my address and subtracted Ellis' age. The answer that I got was weird. It was the same as the last shuttle mission to Hubble.

- - -

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: Friday puzzle -- The Cadets' Mascot

8/1/09, 1:56 PM #3

Alex Yeilding
Guest

Ellis lied about his age ;-)

Interesting method, but you are high by 4.3 feet. The only explanation I have for the discrepancy is in the subject line; I certainly can't fault your methodology!

Re: Friday puzzle -- The Cadets' Mascot

8/1/09, 6:36 PM #4

Dan Donaldson
Member
Offline
5,264 posts

Registered: 9/17/01

hmmm..........

So 125 is not it. Will have to rethink this 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: Friday puzzle -- The Cadets' Mascot

8/1/09, 7:25 PM #5

Alex Yeilding
Guest

Close, but no

Re: Friday puzzle -- The Cadets' Mascot

8/1/09, 9:33 PM #6

Bill Houghton
Member
Offline
8,480 posts

Registered: 1/1/70

100 feet

Re: Friday puzzle -- The Cadets' Mascot

8/1/09, 10:12 PM #7

Alex Yeilding
Guest

Dan was closer

Re: Friday puzzle -- The Cadets' Mascot

8/1/09, 11:26 PM #8

Dan Donaldson
Member
Offline
5,264 posts

Registered: 9/17/01

Re: Dan was closer

Either don't post the answer for awhile, or make sure you mark it well so I don't accidentally read it. I want to play with this one for a bit, but don't have the time right this minute ;-)

- - -

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: Friday puzzle -- The Cadets' Mascot

8/1/09, 11:46 PM #9

Alex Yeilding
Guest

Will Do

Re: Friday puzzle -- The Cadets' Mascot

8/2/09, 8:21 AM #10

Ken Oakley-Sunny St. Cloud, Fla.
Guest

150 feett

Re: Friday puzzle -- The Cadets' Mascot

8/2/09, 12:06 PM #11

Alex Yeilding
Guest

Dan's still closest

Re: Friday puzzle -- The Cadets' Mascot

8/2/09, 2:32 PM #12

Ken Oakley-Sunny St. Cloud, Fla.
Guest

127'

Re: Friday puzzle -- The Cadets' Mascot

8/2/09, 4:41 PM #13

Dan Donaldson
Member
Offline
5,264 posts

Registered: 9/17/01

From your hint

I would guess the answer to be 120.7 feet, but even if this is correct, I still need to work it out. I think I know what has to be done generally, but I need to figure out either how to get it to converge, or an equation that I can solve, at least numerically.

- - -

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: Friday puzzle -- The Cadets' Mascot

8/2/09, 7:44 PM #14

Alex Yeilding
Guest

Another hint

Yes, Dan's got the right answer now.

Solve for the distance the formation travels while the dog is running to the front rank.

Re: Friday puzzle -- The Cadets' Mascot

8/2/09, 7:47 PM #15

Alex Yeilding
Guest

Dan's STILL closest

And in his post below, he gives the actual answer. The question now is how to get there.

Re: Friday puzzle -- The Cadets' Mascot

8/2/09, 9:30 PM #16

Dan Donaldson
Member
Offline
5,264 posts

Registered: 9/17/01

Re: Another hint

I had already done that. This is one of those days when my mind (what there is of it ;-) just doesn't want to work. Going to take a nap and look again. I have a picture and know it is staring me right in the face, but am not seeing it. @#$%#$^$%&%^& ;-)

Will get there yet. At least I will know when I get it ;-)

- - -

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: Friday puzzle -- The Cadets' Mascot

8/3/09, 5:04 AM #17

Alex Yeilding
Guest

The Cadets' Mascot -- Solution, credits and

There are several equivalent ways to set up an equation to solve this one. Here is mine:

Consider the dog's journey in two legs. In the first, the cadets travel x, while the dog travels 50+x to reach the first rank. In the second leg, the dog travels x (to get back to where the front rank started), while the cadets travel 50-x.

Since the dog and the cadets both travel at constant different speeds, the ratio of distances they travel in the same time will always be the same.

This means that(50+x)/x = x/(50-x).

Cross multiplying, x² = 50²-x²

Collecting terms and dividing both sides by 2, x² = 50²/2

Square root of both sides, x = 50/sqrt(2)

The dog's total travel is 50+2x, or 50*(1+sqrt(2)) = 120.7.

Credit: This puzzle came from My Best Mathematical and Logic Puzzles by Martin Gardner.

Another version, credited to Sam Lloyd, has the dog running around the perimeter of the square while the cadets progress 50'. A little more difficult, and considerably more difficult computationally with paper and pencil, but the same basic idea.

Friday puzzle -- The Cadets' Mascot

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