Toughest Logic Puzzle

Toughest Logic Puzzle - 30 October


You are the ruler of a medieval empire and you are about to have a celebration tomorrow. The celebration is the most important party you have ever hosted. You've got 1000 bottles of wine you were planning to open for the celebration, but you find out that one of them is poisoned.

The poison exhibits no symptoms until death. Death occurs within ten to twenty hours after consuming even the minutest amount of poison.

You have over a thousand slaves at your disposal and just under 24 hours to determine which single bottle is poisoned.

You have a handful of prisoners about to be executed, and it would mar your celebration to have anyone else killed.

What is the smallest number of prisoners you must have to drink from the bottles to be absolutely sure to find the poisoned bottle within 24 hours?

Solution 
Fastest Ans : Clive tooth

Best Ans  : I <3 puzlzes & Clive Tooth 

10 prisoners must sample the wine. Bonus points if you worked out a way to ensure than no more than 8 prisoners die.

Number all bottles using binary digits. Assign each prisoner to one of the binary flags. Prisoners must take a sip from each bottle where their binary flag is set.

Here is how you would find one poisoned bottle out of eight total bottles of wine.

Bottle 1 Bottle 2 Bottle 3 Bottle 4 Bottle 5 Bottle 6 Bottle 7 Bottle 8
Prisoner A X X X X
Prisoner B X X X X
Prisoner C X X X X
In the above example, if all prisoners die, bottle 8 is bad. If none die, bottle 1 is bad. If A & B dies, bottle 4 is bad.

With ten people there are 1024 unique combinations so you could test up to 1024 bottles of wine.

Each of the ten prisoners will take a small sip from about 500 bottles. Each sip should take no longer than 30 seconds and should be a very small amount. Small sips not only leave more wine for guests. Small sips also avoid death by alcohol poisoning. As long as each prisoner is administered about a millilitre from each bottle, they will only consume the equivalent of about one bottle of wine each.

Each prisoner will have at least a fifty percent chance of living. There is only one binary combination where all prisoners must sip from the wine. If there are ten prisoners then there are ten more combinations where all but one prisoner must sip from the wine. By avoiding these two types of combinations you can ensure no more than 8 prisoners die.

Google Interview Question

Google Interview Question - 23 October


-> You are given 2 eggs.
-> You have access to a 100-storey building.
-> Eggs can be very hard or very fragile means it may break if dropped from the first floor or may not even break if dropped from 100 th floor.Both eggs are identical.
-> You need to figure out the highest floor of a 100-storey building an egg can be dropped without breaking.
-> Now the question is how many drops you need to make. You are allowed to break 2 eggs in the process

Solution 

Fastest Ans : Gerald Edgar

Best Explained Ans  : Anmol

Toughest Cipher

Toughest Cipher - 15 October
What does this message say?

G T Y O R J O T E O U I A B G T


Hint : Count the letters and try splitting the letters up into groups.

Solution 
This type of code is known as a Caesar Box (Julius Caesar was the first to write codes this way.) To decipher the message, simply divide the code into four groups of four (you can also divide them into groups such as 5 groups of 5 or 6 groups of 6 depending on the number of letters in the phrase), and rearrange them vertically like this...G T Y O
R J O T
E O U I
A B G T

Fastest Ans : Manish Sehjpal

Best Ans  : Sam

Toughest Maths Series

Toughest Maths Series - 10 October

What are the next three numbers in this series?

4, 6, 12, 18, 30, 42, 60, 72, 102, 108, ?, ?, ?

Solution 

First Correct Solution    : Clive Tooth
Best Explained Solution : Lavesh Rawat


138 (137 and 139 are prime), 150 (149 and 151 are prime), 180 (179 and 181 are prime)

The series lists numbers that are flanked by two prime numbers.

4 (3 and 5 are prime)
6 (5 and 7 are prime)
12 (11 and 13 are prime)
18 (17 and 19 are prime)
30 (29 and 31 are prime)
42 (41 and 43 are prime)
60 (59 and 61 are prime)
72 (71 and 73 are prime)
102 (101 and 103 are prime)
108 (107 and 109 are prime)

thus

138 (137 and 139 are prime), 150 (149 and 151 are prime), 180 (179 and 181 are prime)