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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.

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?

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

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?

By Himanshi-Negi

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 ??


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 &