Brainteaser Thursday

[QED]

UPDATE: Both puzzles have been solved... but if you like you can still try your hand at the solution yourself. Just don't scroll too far through the thread, unless you want to see the posted solutions.

First puzzle (solved by hypn0tik):

A young man and his 4-year old son live in a cabin out in the middle of nowhere, exactly 2 miles south of Raging River (which runs East-West). Granny lives nearby roughly to the southeast, exactly 7 miles south of Raging River and exactly 13 miles away from her son's cabin.

The young man wants to travel from his cabin to Granny's, fetching some water from the Raging River for Granny along the way. He figures with he could use some of the Algebra he learned back in high school to help him figure out what the shortest possible path would be, so he draws himself a map and gets to calculating. He quickly learns, though, that his Algebra alone isn't enough to help determine what the shortest path is-- or if there is even one at all! He's just about to give up, when his son comes in and asks him what he's doing. The father show his son the map and explains what he's trying to do. The 4-year old thinks for a moment and says "I can show you the shortest path, Daddy!"-- and then proceeds to draw on the map for about 15 seconds. The man looks, and sure enough he knows for certain that his son has drawn him the shortest possible path. In a matter of a minute, he then uses his basic Algebra knowledge to calculate exactly how many miles he must travel.

How was the son (who obviously has no special math knowledge) able to show his dad the shortest possible path so quickly? And what is the distance the father would travel on this path?




Map (not to scale, X=father/son's house, Y=Grannie's house):

====R=A=G=I=N=G==R=I=V=E=R =====================================


____X

________________Y

Second puzzle (solved by tmc):

The state lottery offers a second-chance promotion for losing lottery tickets. On the back of every lottery ticket is a random 4-digit serial number. If you bring in 1 or more losing lottery tickets from the same day whose serial numbers (NOT the digits) sum up to a multiple of 7, you win $5. How many losing lottery tickets from a particular day will you have to collect before you are guaranteed of winning the $5?

EDIT: Assume all serial numbers are unique (i.e., not repeated) for each day. This will obviously mean that there are at most 10,000 losing lottery tickets out there each day.

 

[Anubis]

nice try but im not gonna do your homework

 

[DisgruntledVirus]

Originally posted by: Anubis
nice try but im not gonna do your homework

And the point goes to.....

Drum roll....

Anubis

 

[QED]

Originally posted by: Anubis
nice try but im not gonna do your homework

I have a PhD in mathematics... trust me, the only homework I'm doing anymore is when I'm tutoring someone.

Besides, the answer is so quick and easy a 4-year old could do it... heck-- I bet a liberal arts major could even do it!
:evil:

 

[Anubis]

Originally posted by: QED

Originally posted by: Anubis
nice try but im not gonna do your homework

I have a PhD in mathematics... trust me, the only homework I'm doing anymore is when I'm tutoring someone.

Besides, the answer is so quick and easy a 4-year old could do it... heck-- I bet a liberal arts major could even do it!
:evil:

you have a PhD in math and cant figure out how to turn on the sarcasm meter

 

[QED]

Originally posted by: Anubis

Originally posted by: QED

Originally posted by: Anubis
nice try but im not gonna do your homework

I have a PhD in mathematics... trust me, the only homework I'm doing anymore is when I'm tutoring someone.

Besides, the answer is so quick and easy a 4-year old could do it... heck-- I bet a liberal arts major could even do it!
:evil:

you have a PhD in math and cant figure out how to turn on the sarcasm meter

Sorry... that requires a little common sense, and I've been told repeatedly that I have none.

This was me back in high school...

 

[Injury]

umm... draw a line between the houses?

No one is asking for the distance.

edit: Admittedly... I skimmed. I would think that the shortest distance would make a right angle from the path to and from the river as you're always making maximum progress towards grandma's that you can.

 

[Beev]

If the house is 13 miles away wouldn't the shortest path be 13 miles? You can't move the house closer.

<- Not a math person.

Edit: Oh, he has to get water first

 

[QED]

Originally posted by: Injury
umm... draw a line between the houses?

Aye... the only rub is that he has to stop at the river somewhere along the way. But where?

 

[hypn0tik]

My guess would be where the first 'G' in Raging River of your figure.

Reflect point X onto the other side of the river and call it X'. Join X' with Y to find the point on the river that he must walk to fetch water.

Edit: Distance is 15 miles.

 

[FP]

He can walk 2 miles north to get the water... Hop in a raft and paddle upstream 12 miles at which point he will be directly north of grandma's house. He gets out and walks 7 miles south.

Total walking distance is 9 miles.

 

[hypn0tik]

Originally posted by: binister
He can walk 2 miles north to get the water... Hop in a raft and paddle upstream 12 miles at which point he will be directly north of grandma's house. He gets out and walks 7 miles south.

Total walking distance is 9 miles.

They're asking for shortest distance traveled, not shortest walking distance.

 

[QED]

Originally posted by: binister
He can walk 2 miles north to get the water... Hop in a raft and paddle upstream 12 miles at which point he will be directly north of grandma's house. He gets out and walks 7 miles south.

Total walking distance is 9 miles.

Dahh! I was just about to declare hypn0tik the winnar until I read this. If I ever teach math again, this is the answer I'll expect when offering this puzzle (with slight modification) for extra credit...

 

[Injury]

Originally posted by: QED

Originally posted by: Injury
umm... draw a line between the houses?

Aye... the only rub is that he has to stop at the river somewhere along the way. But where?

If Granny lives a 14 mile trip to the river and back, and the guy lives a 13 mile trip from Granny's, then Granny should go get the water for him while he's on his way over. Grandmas are like that. They'll go out of their way to help, especially if it means they get to see their family.

 

[Atomic Playboy]

They shouldn't drink that river water, they'll get giardhia. Buy a Brita granny.

 

[TuxDave]

Bah, already solved above.

 

[TuxDave]

Originally posted by: binister
He can walk 2 miles north to get the water... Hop in a raft and paddle upstream 12 miles at which point he will be directly north of grandma's house. He gets out and walks 7 miles south.

Total walking distance is 9 miles.

WIN!

 

[MikeyLSU]

go straight to river, 2 miles.

Then striaght line to granny's, 13.89 miles.

Total 15.89 miles.

 

[FP]

Originally posted by: QED

Originally posted by: binister
He can walk 2 miles north to get the water... Hop in a raft and paddle upstream 12 miles at which point he will be directly north of grandma's house. He gets out and walks 7 miles south.

Total walking distance is 9 miles.

Dahh! I was just about to declare hypn0tik the winnar until I read this. If I ever teach math again, this is the answer I'll expect when offering this puzzle (with slight modification) for extra credit...

My answer isn't correct is it? The question didn't specify walking distance, I was just being a jackass . Plus paddling upstream against a "raging river" would be 100x harder than walking an extra 6 miles.

Got any more? I love these kinds of problems...

 

[SaoFeng]

Originally posted by: Injury

Originally posted by: QED

Originally posted by: Injury
umm... draw a line between the houses?

Aye... the only rub is that he has to stop at the river somewhere along the way. But where?

If Granny lives a 14 mile trip to the river and back, and the guy lives a 13 mile trip from Granny's, then Granny should go get the water for him while he's on his way over. Grandmas are like that. They'll go out of their way to help, especially if it means they get to see their family.

ahahah best answer

 

[dainthomas]

Originally posted by: MikeyLSU
go straight to river, 2 miles.

Then striaght line to granny's, 13.89 miles.

Total 15.89 miles.

Hitting the river 6 miles east then heading southeast to grandma's would be 15.54 mi.

 

[EarthwormJim]

Originally posted by: binister
He can walk 2 miles north to get the water... Hop in a raft and paddle upstream 12 miles at which point he will be directly north of grandma's house. He gets out and walks 7 miles south.

Total walking distance is 9 miles.

The river flows east-west and it's "raging," so I don't think he can paddle against it.

 

[Mr Pickles]

8====R=A=G=I=N=G==B=O=N=E=R =====================================D ~~~~~~~~~~~

 

[KB]

I did a couple iterations and best I could do was:
Head Northeast so you come to the river two miles north and three miles east of home: 3.6055~ miles
Then head Southeast toward grandmas: 11.401754~ miles
total trip: 15.00725~ miles

I bet there is a sweet spot between 2 and 4 miles east but I am too lazy to find it.

 

[tmc]

the straight line distance from X to Z is the answer, with Z being the mirror image of Y on the other side of the river (with the river as the mirror).