Toughest Math Statement Question

Toughest Math Statement Puzzle / Question

I am thinking of a 6-digit number. The sum of the digits is 43.

And only two of the following three statements about the number are true:

(1) it's a square number,
(2) it's a cube number, and
(3) the number is under 500000.


Solution 
Discuss Below

Toughest Sherlock Holmes Question

Toughest Sherlock Holmes  Question 

Sherlock, A detective who was mere days from cracking an international smuggling ring has suddenly gone missing. While inspecting his last-known location, you find a note:
710 57735 34 5508 51 7718
Currently there are 3 suspects: Bill, John, and Todd. Can you break the detective's code and find the criminal's name?

Solution
Bill. If you read the message upside down, 
you'll notice that the numbers resemble letters and that those letters form legible sentences. 
The message is 'Bill is boss. He sells oil.'


Solution By



Greentulip05 , Noone , Michael Beck

&

http://dailybrainteaser.blogspot.com/2011/10/sherlock-holmes-cipher-
puzzle.html

Toughest Probability Question

Toughest Probability Puzzle / Question

How many people must be gathered together in a room, before you can be certain that there is a greater than 50/50 chance that at least two of them have the same birthday?

Solution 
By Himanshi-Negi
&
http://dailybrainteaser.blogspot.com/2011/07/probability-of-having-same-birthday.html

Only twenty-three people need be in the room, a surprisingly small number. The probability that there will not be two matching birthdays is then, ignoring leap years, 365x364x363x...x343/365 over 23 which is approximately 0.493. this is less than half, and therefore the probability that a pair occurs is greater than 50-50. With as few as fourteen people in the room the chances are better than 50-50 that a pair will have birthdays on the same day or on consecutive days.

Toughest Popular Question

Toughest Popular Puzzle / Question 


Outside a room there are three light switches. One of switch is connected to a light bulb inside the room.
Each of the three switches can be either 'ON' or 'OFF'.

You are allowed to set each switch the way you want it and then enter the room(note: you can enter the room only once)

Your task is to then determine which switch controls the bulb ??

Solution 

Set the first switches on for abt 10min, and then switch on the second switch and then enter the room.
Three cases are possible
1.Bulb is on => second switch is the ans
2.Bulb is off and on touching bulb , you will find bulb to be warm
=>1st switch is the ans.
3.Bulb is off and on touching second bulb , you will find bulb to be normal(not warm)
=>3rd bulb is the ans.


By Dumanshu Goyal & 
http://dailybrainteaser.blogspot.com/2011/08/challenging-puzzle.html

Toughest Microsoft Interview Question

Toughest Microsoft Interview Puzzle / Question - 29th November

The puzzle question is : On Bagshot Island, there is an airport. The airport is the homebase of an unlimited number of identical airplanes. Each airplane has a fuel capacity to allow it to fly exactly 1/2 way around the world, along a great circle. The planes have the ability to refuel in flight without loss of speed or spillage of fuel. Though the fuel is unlimited, the island is the only source of fuel.
What is the fewest number of aircraft necessary to get one plane all the way around the world assuming that all of the aircraft must return safely to the airport? How did you get to your answer?
Notes:
(a) Each airplane must depart and return to the same airport, and that is the only airport they can land and refuel on ground.
(b) Each airplane must have enough fuel to return to airport.
(c) The time and fuel consumption of refueling can be ignored. (so we can also assume that one airplane can refuel more than one airplanes in air at the same time.)
(d) The amount of fuel airplanes carrying can be zero as long as the other airplane is refueling these airplanes. What is the fewest number of airplanes and number of tanks of fuel needed to accomplish this work? (we only need airplane to go around the world)

Solution 
By DaveDodson & WEBSITE

http://dailybrainteaser.blogspot.com/2011/07/aeroplane-hardest-quiz.html

As per the puzzle given above The fewest number of aircraft is 3!

Imagine 3 aircraft (A, B and C). A is going to fly round the world. All three aircraft start at the same time in the same direction. After 1/6 of the circumference, B passes 1/3 of its fuel to C and returns home, where it is refueled and starts immediately again to follow A and C.

C continues to fly alongside A until they are 1/4 of the distance around the world. At this point C completely fills the tank of A which is now able to fly to a point 3/4 of the way around the world. C has now only 1/3 of its full fuel capacity left, not enough to get back to the home base. But the first 'auxiliary' aircraft reaches it in time in order to refuel it, and both 'auxiliary' aircraft are the able to return safely to the home base.

Now in the same manner as before both B and C fully refuelled fly towards A. Again B refuels C and returns home to be refuelled. C reaches A at the point where it has flown 3/4 around the world. All 3 aircraft can safely return to the home base, if the refuelling process is applied analogously as for the first phase of the flight.

Toughest Picture Question

Toughest Picture Puzzle(Question)


Below the four parts have been reorganized. The four partitions are exactly the same in both arrangements. Why is there a hole?





Solution 


By Author
The gradient of the teal hypotenuse is different than the gradient of the red hypotenuse.

Toughest Brain Question

Toughest Brain Twister Question - 14 November


2+3=8,
3+7=27,
4+5=32,
5+8=60,
6+7=72,
7+8=??
Solve it ?

Solution 
Fastest (Amit Singh)
By  Tomasz Budzeń (Best Explained)


n A B C=A-B C(n) - C(n-1) = 2

0 2
1 2 + 3 = 8 2*3 = 6 2 4
2 3 + 7 = 27 3*7 = 21 6 6
3 4 + 5 = 32 4*5 = 20 12 8
4 5 + 8 = 60 5*8 = 40 20 10
5 6 + 7 = 72 6*7 = 42 30 12 
6 7 + 8 = ?? 7*8 = 56 (42) 

(Pascal's difference machine)

A(n) = 
B(n) + C(n) = a(n) * b(n) + C(n) = a(n) * b(n) + (n-1) * (n-2) = (n+1) * b(n) + n * (n+1)

So:

A(n) = (n + 1) * (b(n) + n) [it doesn't depend on a]

And:

A(6) = 7 * (8 + 6) = 7 * 14 = 98