purplethunder3121 said:

Could you work for Google? If you can solve the '100 hat riddle' you're in with a chance

• 13:30, 3 MAR 2016


• UPDATED 15:08, 3 MAR 2016


• BY ZAHRA MULROY

Artificial intelligence has no problem coming up with the answer - but can you?

Are you smart enough to work for Google? Solve the riddle below

While the rigour of the questions asked in job interviews may vary, there are some stock favourites which come up again and again.

What are your three greatest strengths and weaknesses? And the perennial classic: Where do you see yourself in five years time?

But if you want a job at Google, you'll need more than your five year plan to cut the mustard - their interview involves solving a fiendish riddle which artificial intelligence has no problem getting to the bottom of.

Have your say in the comments section below

The 100 hat riddle

Jakob Foerster

Google interview hat riddle - can you come up with a solution?

1. 100 prisoners stand in line, one in front of the other, each wearing either a red hat or a blue hat.

2. Every prisoner can see the hats of the people in front but not their own hat, or the hats worn by anyone behind.

3. A prison guard starts at the back of the line and asks each prisoner the colour of their hat. If they answer correctly, they will be pardoned, if they get it wrong, they’ll be executed.

4. Before lining up, the prisoners are allowed to collectively come up with a strategy.

What should they do?

The good news is, there IS a way for 99 of the prisoners to definitely survive and the remaining prisoner to have a respectable shot at 50 per cent.

• 
  

  To get this result, the first prisoner in the line must say "blue" if he sees an even number of hats in front of him.

  
  


• 
  

  If he sees an odd number of hats in front of him, he must say "red".

  
  


• This information, coupled with the responses other prisoners have already given and the hats in front is enough to work out what colour hat is on your head.

So, everyone except the first prisoner will definitely answer correctly

A team from the University of Oxford and Google's DeepMind created an AI (artificial intelligence) to tackle the riddle - and it cracked it.

Getty

Artificial Intelligence can get a job at Google no problem

If you love puzzles, but would like to have a go at something humans can solve, see if you can crack this simple brainteaser designed for children - which got the better of a lot of adults.

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16 on the fruit

i have no idea why the answer (100 hats)

would be 'red' 'red'

........................................................

fruit math: 14

the hat one seems to be like the loins and sheep riddle

there seems to be something wrong with the question. Saying "blue" or "red" based on the number of total hats is not helpful... they would all know how many were in fount of them...anyway there is something eles to this riddle...

um... i googled the answer:

.

The solution

For the sake of explanation let's label the prisoners in line order B, C and D. Thus C can see B (and B's hat color) and D can see B and C.

The prisoners know that there are only two hats of each color. So if D observes that B and C have hats of the same color, D would deduce that his own hat is the opposite color. However, if B and C have hats of different colors, then D can say nothing. The key is that prisoner C, after allowing an appropriate interval, and knowing what D would do, can deduce that if D says nothing the hats on B and C must be different. Being able to see B's hat he can deduce his own hat color.

In common with many puzzles of this type, the solution relies on the assumption that all participants are totally rational and are intelligent enough to make the appropriate deductions.

After solving this puzzle, some insight into the nature of communication can be gained by pondering whether the meaningful silence of prisoner D violates the "No communication" rule (given that communication is usually defined as the "transfer of information").

Fruit is 15.

The fruit is 14.

1 coconut half = 1, 1 apple = 10, 3 bananas = 3.

It's a trick on scanning ability. (Sorry scanning and reasoning ability)




I don't get the reasoning about the hats yet. Maybe I'll make an effort maybe I won't.

[Edited 3/4/16 10:23am]

KingBAD said:

16 on the fruit

i have no idea why the answer (100 hats)

would be 'red' 'red'

........................................................

i got sixteen too.

apple = 10

banana bunch = 4

coconut half =2

There are only 3 bananas on the last equation as opposed to 4 in the previous equations. Also half as many coconuts as before.


3 Apples = 30 which is 10 per apple

apple (10) + 4 bananas (4) + 4 bananas (4) = 18

4 bananas (4) - 2 coconut halves (2) = 2

1 coconut half (1) + apple (10) + 3 bananas (3) = 14

Okay this right here makes no sense to me:

- To get this result, the first prisoner in the line must say "blue" if he sees an even number of hats in front of him.



If there are 100 prisoners and the first one can see everyone in front of him, wouldn't he see 99 prisoners? So that's odd, therefore he can't say "blue" he'd have to say "red". But if that's the solution then how is there a guarantee for 99 other prisoners if the color of the hats are randomly lined up?

I mean the picture above the 3rd hat would say "red" then the next would say "blue" then "red" then "blue" but that only works if they are lined up alternating.


I don't get it.

Hudson said:

There are only 3 bananas on the last equation as opposed to 4 in the previous equations. Also half as many coconuts as before.


3 Apples = 30 which is 10 per apple

apple (10) + 4 bananas (4) + 4 bananas (4) = 18

4 bananas (4) - 2 coconut halves (2) = 2

1 coconut half (1) + apple (10) + 3 bananas (3) = 14

It's obvious now that you point it out. That's why I got 15 instead of 14. Boy, my powers of observation ain't as sharp as they used to be. Forget the 100 hats!

purplethunder3121 said:

Hudson said:

There are only 3 bananas on the last equation as opposed to 4 in the previous equations. Also half as many coconuts as before.


3 Apples = 30 which is 10 per apple

apple (10) + 4 bananas (4) + 4 bananas (4) = 18

4 bananas (4) - 2 coconut halves (2) = 2

1 coconut half (1) + apple (10) + 3 bananas (3) = 14

It's obvious now that you point it out. That's why I got 15 instead of 14. Boy, my powers of observation ain't as sharp as they used to be. Forget the 100 hats!

me too. i only glanced at it. couldn't work for google. oh well

{To make sure most of them survive, the prisoners must agree on the message communicated with each colour. The first prisoner to speak will say blue if the number of blue hats he sees in front of him is even, or red if he sees otherwise.}


Would that work?

Screw that NASA wants to pay me $1,200 a week to lay in bed and smoke weed.

lazycrockett said:

Screw that NASA wants to pay me $1,200 a week to lay in bed and smoke weed.

And there you go.

XxAxX said:

um... i googled the answer:

.

:facepalm: Talk about delayed reaction. Sometimes I wonder about me.

RodeoSchro said:

Fruit is 15.

14

lazycrockett said:

Screw that NASA wants to pay me $1,200 a week to lay in bed and smoke weed.

Damn skippy,

lazycrockett said:

Screw that NASA wants to pay me $1,200 a week to lay in bed and smoke weed.

Where does one apply?

i think folks look and still miss the thing...

apples= 10

bananas= 4

coconuts= 2

2+10+4= 16 everywhere i ever been...

OnlyNDaUsa said:

fruit math: 14

the hat one seems to be like the loins and sheep riddle

i know how hard it is for you to just accept what i say

so i drew you a map...

the answer is 16

XxAxX said:

KingBAD said:

16 on the fruit

i have no idea why the answer (100 hats)

would be 'red' 'red'

........................................................

i got sixteen too.

apple = 10

banana bunch = 4

coconut half =2

you ever notice

that it's basically the same people

they have the most to say on 'other' subjects

so vehemately (no matter how wrong)

are pretty much the same folks that cannot

GET THIS

i really do love walkin through puddles

KingBAD said:

XxAxX said:

i got sixteen too.

apple = 10

banana bunch = 4

coconut half =2

you ever notice

that it's basically the same people

they have the most to say on 'other' subjects

so vehemately (no matter how wrong)

are pretty much the same folks that cannot

GET THIS

i really do love walkin through puddles

the irony is the answer is 14...you are mistaken. See each coconut half is 1, each banana is 1, and each apple is 10.

1+10+ (1+1+1)= 14

just like

10+10+10 = 30

10 + (1+1+1+1) + (1+1+1+1) = 18

(1+1+1+1) - (1+1) = 2

1+10+ (1+1+1)= 14

you just do not get the trick is in the number of coconut halves and you number of bananas is the different bunches....

I did a topic on this trick math things a wile back:

like what is 1 X 2 + 3 x 4 + 5 x 0 + 1?

KingBAD said:

OnlyNDaUsa said:

fruit math: 14

the hat one seems to be like the loins and sheep riddle

i know how hard it is for you to just accept what i say

so i drew you a map...

the answer is 16

:lol:

the irony is you did not read the legend on your own map and you got lost along the way.

the answer is 14

it is fine to point out when someone makes an error. I respect that. I can accept being wrong. But in doing so, how one goes about it is important. It is important to not over do it becase as is the case here if you are in error and you are mocking in how you made the 'correction' it really makes you look worst.

KingBAD said:

i think folks look and still miss the thing...

apples= 10

bananas= 4

coconuts= 2

2+10+4= 16 everywhere i ever been...

ok i can not help it but YES i am replying to all 3 of KB's replies:

an apple is 10 (well we assume it is a whole apple)
a bunch of 4 bananas is 4
and 2 coconut halves are 2

In the last sentence we have one coconut half, an apple, and a bunch of 3 bananas- for a totall established value of 14.

KingBAD said:

OnlyNDaUsa said:

fruit math: 14

the hat one seems to be like the loins and sheep riddle

i know how hard it is for you to just accept what i say

so i drew you a map...

the answer is 16

.

this is one of those trick questions they throw on IQ tests. it is not a measure of intelligence, it is a measure of whether or not you are paranoid enough to expect a trick question.

.

it's not about math, it's about whether you noticed that only one half of the coconut, and only three bananas instead of four, are in the bunches in the last question.

.

once a person comes to expect trick questions, they are easy to solve.

XxAxX said:

KingBAD said:

i know how hard it is for you to just accept what i say

so i drew you a map...

the answer is 16

.

this is one of those trick questions they throw on IQ tests. it is not a measure of intelligence, it is a measure of whether or not you are paranoid enough to expect a trick question.

.

it's not about math, it's about whether you noticed that only one half of the coconut, and only three bananas instead of four, are in the bunches in the last question.

.

once a person comes to expect trick questions, they are easy to solve.

it has to be either a trick or rely on a common error people make. Like what is 1 X 2 + 3 x 4 + 5 x 0 + 1 = ? not a trick but dose allow for a basic common error.