This problem was inspired by the wonderful brain teasers of Ice Pie. Thank you for your inspiration.
Joe Doodlebug is a somewhat strange bug, who lives in a different world from us. These are his capabilities and limitations in his world:
1 - his world is flat
2 - He can only jump (not crawl, walk, roll or otherwise)
3 - He cannot turn around
4 - he can jump any distance between 1 inch and 500 feet per jump
5 - he can jump in only four perfectly true directions - north, south, east, west (he cannot jump diagonally northeast, southwest etc)
6 - he likes to average 15 feet per jump on a good day
7 - once he starts in any direction - he must complete four jumps in that directionbefore he can switch to another direction
8 - there are no other doodlebugs or any other creatures to help Joe
9 - Joe is totally dependant on his owner to provide his food
10 - Joe always takes the fewest possible jumps to get to his food
The Problem:
Joe has been out jumping and is now getting hungry. His owner places some food down for Joe. Joe is facing north. The food is 3 feet away and directly west of Joe. Realising at this point Joe could not jump due west, he explaims "I have it, I must jump 4 times to reach the food in the fewest number of jumps"
Accepting the fact that Joe is a smart bug and his conclusion is correct - why did he need to jump four times and what where the circumstances that brought Joe to this conclusion?
Why can't he jump directly west when the rules say he can only jump north, south, east and west?
I'm confused. Too much ice cream perhaps??
:P
PS in edit - ah, he's FACING north and can't turn round!
More ice cream needed for thinking purposes!
thats Joe's problem sorted
NEXT!!!
Okay, okay
too much vodka and wheat beer , this is now making my head hurt!!!!!!!!!!
OK, how about this.
Joes does NOT have to jump in the direction he's facing, nor does he have to face the direction he's jumping in. The rules don't disallow this so I'm assuming it's true.
If Joe can't jump west it must be because he is in the middle of a sequence of jumps in some other direction. I'm treating the fact that he's facing north as a red herring because it's not relevant according to the wording of the rules.
So, Joe is facing north (irrelevant) and he's just jumped east. To get to the food he must make a further 3 jumps east, then a big jump west. The 15ft average is also a red herring because it doesn't say it's obligatory and it doesn't say how many jumps must satisfy this average, but if it were obligatory, there are infinitely many solutions that give a 60ft total for 4 jumps or a 75ft total for 5 jumps.
One i heard a while ago - hope i can remeber it right!!
3 people book into a hotel and share the cost of a room
When they book in they are told the cost is £30
so they all chip in a tenner each.
After a few hours the managers remebers that there's a special offer on and the room should have been £25 so he gives the porter the £5 to give back to the guests.
On the way to the room the porter thinks the guests will find it hard to separate the £5 between the 3 of them so does them a favour and pockets £2 so each guest gets a £1 each.
So all in all the guests have paid a total of £9 pound each - £27 the porter has £2 a total of £29 - where's the missing pound from the original £30?