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?
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Inspired by Ice Pie
Sex God
According to the rules, he can jump 3 feet directly west, pick up the food, then do three more jumps west any distance he likes, then do whatever he wants. 
Sex God
Quote by Jags
PS in edit - ah, he's FACING north and can't turn round!
If he is restricted to only jumping in the direction he's facing, that would mean he can only ever jump north, but the rules don't say that, so he can jump sideways.
Quote by Ice Pie
According to the rules, he can jump 3 feet directly west, pick up the food, then do three more jumps west any distance he likes, then do whatever he wants.
Not so.......
Joe's situation - he is currently facing north, the food is due west, he cannot jump due west at his time - remember once he starts to jump in any direction he must complete a sequence of four jumps in the same direction before he can alter his direction!
Sex God
Quote by PoloLady
According to the rules, he can jump 3 feet directly west, pick up the food, then do three more jumps west any distance he likes, then do whatever he wants.
Not so.......
Joe's situation - he is currently facing north, the food is due west, he cannot jump due west at his time - remember once he starts to jump in any direction he must complete a sequence of four jumps in the same direction before he can alter his direction!
So he can only jump in the direction he's facing? Rule 3 says he can't turn round - does that mean he only ever faces north, or does it mean he can't do an about face?
Sex God
thats Joe's problem sorted
NEXT!!!
Quote by Ice Pie
According to the rules, he can jump 3 feet directly west, pick up the food, then do three more jumps west any distance he likes, then do whatever he wants.
Not so.......
Joe's situation - he is currently facing north, the food is due west, he cannot jump due west at his time - remember once he starts to jump in any direction he must complete a sequence of four jumps in the same direction before he can alter his direction!
So he can only jump in the direction he's facing? Rule 3 says he can't turn round - does that mean he only ever faces north, or does it mean he can't do an about face?
the rule is - once he starts to jump in any direction he must continue for a total of four jumps in the same direction before he alters his direction.
Sex God
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.
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.
Quote by Ice Pie
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.
woo hooooooo
but then you are a brain box
Don't inspire me again - that was the best I could come-up with
Sex God
Quote by PoloLady
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.
woo hooooooo
but then you are a brain box
Don't inspire me again - that was the best I could come-up with
Ooooh, that was devious. The rules kind of lead you into some assumptions that aren't actually stated. It's only when you reject those assumptions you can see the answer. I like that.
Got any more? Quote by Ice Pie
Ooooh, that was devious. The rules kind of lead you into some assumptions that aren't actually stated. It's only when you reject those assumptions you can see the answer. I like that.
I use a few of them at work - 'thinking outside of the box' problems - it is always the assumptions that stop people from seeing a solution - but isn't that life!
I bet you know the one with a farmer who has a bag of corn, a chicken and a fox, and needs to cross a river in a boat!
By the way - you can inspire me all you want
Sex God
Quote by PoloLady
Ooooh, that was devious. The rules kind of lead you into some assumptions that aren't actually stated. It's only when you reject those assumptions you can see the answer. I like that.
I use a few of them at work - 'thinking outside of the box' problems - it is always the assumptions that stop people from seeing a solution - but isn't that life!
I bet you know the one with a farmer who has a bag of corn, a chicken and a fox, and needs to cross a river in a boat!
By the way - you can inspire me all you want
I'm not familiar with the boat problem, but it sounds similar to the cannibals/missionaries thing: You can't tleave the fox alone with the chicken and you can't leave the chicken alone with the corn and there's only room in the boat for two things?
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?
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?
Sex God
Quote by AndyS-NE
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?
There is no missing pound: The Manager has £25, the porter has £2 and the guests have a pound each. Total £30
The wording of the question is deceptive. The £2 that the porter has is included in the £27 the guests have paid, so there's only £3 to be accounted for and that's their change.
Ice
Quote by AndyS-NE
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?
I had forgot about that one - I will be using it soon though - maybe try and screw-up the loss prevention team 