Brain Teasers

[Oorang]

That is why it's in the order it is.

 

[GorD]

I think everbody knows this one

4 hostages being held by an armed guard. 3 are one side of a wall and the other is on the other. Each has had a hat put on their head, there are two blue hats and two red hats. Everyone is facing the wall and can't turn round. The guard says that if anyone can correcly guess the colour of their hat the will all be saved, but if anyone guesses wrongly they will all be killed.
Who shoulld call out their colour to guarantee their safety.


x.................x......................x......................¦......................x

 

[Scott Huish]

Can the person by himself see over the wall?

If so, then he can see what the other three hats are and he should call his own color based on this information.

 

[GorD]

No He can't

As a bit of a clue, the person to call out can be one of two people depending on the circumstance

Also just to clarify in case it wasn't clear, the person furthest from the wall can see the two in front, and the middle person can see the one in front of him

 

[Oaktree]

If the guy farthest from the wall sees two hats of the same color (say, red), he knows his is of the opposite color (blue).

If the guy farthest from the wall hesitates/doesn't say anything, the middle guy would know that he has a different colored hat than the one guy he can see and could speak up accordingly.

Here's one for you (from Seth Godin's blog):

Let's say your goal is to reduce gasoline consumption.

And let's say there are only two kinds of cars in the world. Half of them are Suburbans that get 10 miles to the gallon and half are Priuses that get 50.

If we assume that all the cars drive the same number of miles, which would be a better investment:

(1) Get new tires for all the Suburbans and increase their mileage a bit to 13 miles per gallon.
(2) Replace all the Priuses and rewire them to get 100 miles per gallon (doubling their average!)

 

[Cindy Ellis]

Let's say your goal is to reduce gasoline consumption.

And let's say there are only two kinds of cars in the world. Half of them are Suburbans that get 10 miles to the gallon and half are Priuses that get 50.

If we assume that all the cars drive the same number of miles, which would be a better investment:

(1) Get new tires for all the Suburbans and increase their mileage a bit to 13 miles per gallon.
(2) Replace all the Priuses and rewire them to get 100 miles per gallon (doubling their average!)

Tires win
For every thousand milles driven by each group, increasing the Suburban mpg by 30% ( 10 mpg to 13 mpg) reduces gas consumption by ~23 gallons, while doubling the mpg of the prius group (50 mpg to 100 mpg) only saves 10 gallons.

 

[Scott Huish]

This question has 2 possible answers.

1. Reducing gasoline consumption

or

2. Reduction Percentage to the vehicles standard MPG

If you go with option 2 then Cindy is correct, but if you go with option 1, then the Prius is still the best investment, because you will reduce gasoline consumption overall.

In other words, while the GMC reduced its gasoline usage by more gallons, it still used way more gasoline than the Prius.

At it's best it uses approximately 76 gallons of gasoline, while the Prius only uses 10. I would go with the Prius.

Excel Workbook
	A	B	C	D
1	Miles Driven: 1000
2
3
4	Suburban	Gallons Used	Prius	Gallons Used
5	10 mpg	100	50 mpg	20
6	13 mpg	76.92307692	100 mpg	10
7	Gallons Saved	23.08		10
8	(Rounded to 2 decimal places)
Sheet1

 

[Scott Huish]

Correction, the Suburban used more gasoline overall.

 

[Cindy Ellis]

??
The way I read it, we don't get to change the proportion of cars or the proportion of miles driven (50/50 proportion, and equal miles driven by each), so the best investment for "society" or for a company trying to reduce gasoline consumption would be to do the tire change.
Before any change, 2000 miles driven overall (half by prius and half by suburban) would require 120 gallons of gas. If we invest in doubling the mpg of prius, with no other change, the same 2000 miles would now require 110 gallons of gas. On the other hand, if we change the tires on the suburban to magic tires that get 13 mpg instead of 10 mpg, the same 2000 miles requires only ~87 gallons of gas.

 

[Scott Huish]

My example uses the same number of miles for both vehicles: 1000

For the Suburban to travel 1000 miles at 13 mpg, it takes a little less than 77 gallons to do it.

A Prius to travel 1000 miles at 100 mpg, takes 10 gallons.

The car that takes 10 gallons to drive a 1000 miles uses significantly less gasoline than the vehicle that travels at 13 mpg.

Since the goal is to reduce gasoline consumption, the Prius does a better job of this than the Suburban does.

Before any change both vehicles combined used 120 gallons of gas.
After both vehicles were changed, the combined usage of gasoline was approximately 86.92 gallons, the majority of this was used by the Suburban. The Prius only using 10 gallons of it.

You can pick any mileage amount you want as long as they are equal for both vehicles, but proportionately the results will be the same.