# Monkey and Lamp Puzzle

1,124.8K Views

A very big building in which thousand monkeys are living is lighted by thousand lamps. Every lamp is connected to a unique on/off switch, which are numbered from 1 to 1000. At some moment, all lamps are switched off. But because it is becoming darker, the monkeys would like to switch on the lights. They will do this in the following way.

Monkey 1 presses all switches that are a multiple of 1.
Monkey 2 presses all switches that are a multiple of 2.
Monkey 3 presses all switches that are a multiple of 3.
Monkey 4 presses all switches that are a multiple of 4.
Etc., etc.

How many lamps are switched on after monkey 1000 pressed his switches?
And
which lamps are switched on?

SherlockHolmes Expert Asked on 21st October 2015 in

Only the lights connected to switches with a number that has an odd number of factors are left on.  These are the square numbers.  The largest square square number less than 1000 is 31^2 = 961, so there are 31 lights on connected to the switches 1^2, 2^2, … 31^2.

dougbell Genius Answered on 21st October 2015.

/*
Yep Thats Perfect!
Following is a java program to do the same thing.
*/
class k1{
public static int[] factorize (int a[], int p)
{
int count=0,no=p;
int b[]= new int[a.length];
b=a;
for(int i=2;i<=p;i++)
if(p%i==0){b[count++]=i;}
b[count++]=1;
return b;
}

public static int no_of_factors(int b[])
{
int counter=0;
for(int i=0;i<b.length-1;i++)
{
if(b[i+1]!=b[i]&&b[i]!=0) counter++;
}
return counter;
}

public static void main(String args[])
{
int on_count=0;
int a[]= new int[50];
for(int i=1;i<=1000;i++)
{
factorize(a,i);
int x = no_of_factors(a);
if(x%2!=0) on_count++;
for(int j=0;j<50;j++)a[j]=0;
}

System.out.print(on_count);

}// end of main
}// end of class

Vinayak Scholar Answered on 23rd November 2015.

• ## More puzzles to try-

• ### What is the logic behind these ?

3 + 3 = 3 5 + 4 = 4 1 + 0 = 3 2 + 3 = 4 ...Read More »
• ### Defective stack of coins puzzle

There are 10 stacks of 10 coins each. Each coin weights 10 gms. However, one stack of coins is defective ...Read More »
• ### Which clock works best?

Which clock works best? The one that loses a minute a day or the one that doesn’t work at all?Read More »
• ### (Advanced) Cheryl’s Birthday Puzzle

Paul, Sam and Dean are assigned the task of figuring out two numbers. They get the following information: Both numbers ...Read More »
• ### Five greedy pirates and gold coin distribution Puzzle

Five  puzzleFry ship’s pirates have obtained 100 gold coins and have to divide up the loot. The pirates are all ...Read More »
• ### Tuesday, Thursday what are other two days staring with T?

Four days are there which start with the letter ‘T‘. I can remember only two of them as “Tuesday , Thursday”. ...Read More »
• ### How could only 3 apples left

Two fathers took their sons to a fruit stall. Each man and son bought an apple, But when they returned ...Read More »
• ### How Many Eggs ?

A farmer is taking her eggs to the market in a cart, but she hits a  pothole, which knocks over ...Read More »
• ### Most Analytical GOOGLE INTERVIEW Question Revealed

Let it be simple and as direct as possible. Interviewer : Tell me how much time (in days) and money would ...Read More »
• ### Lateral thinking sequence Puzzle

Solve this logic sequence puzzle by the correct digit- 8080 = 6 1357 = 0 2022 = 1 1999 = ...Read More »
• ### How did he know?

A man leaves his house in the morning to go to office and kisses his wife. In the evening on ...Read More »
• ### Pizza Cost Math Brain Teaser

Jasmine, Thibault, and Noah were having a night out and decided to order a pizza for \$10. It turned out ...Read More »
• ### Which letter replaces the question mark

Which letter replaces the question markRead More »
• ### Which room is safest puzzle

A murderer is condemned to death. He has to choose between three rooms. The first is full of raging fires, ...Read More »
• ### Richie’s Number System

Richie established a very strange number system. According to her claim for different combination of 0 and 2 you will ...Read More »
• ### Srabon wanted to pass

The result of math class test came out. Fariha’s mark was an even number. Srabon got a prime!! Nabila got ...Read More »
• ### Become Normal!!

Robi is a very serious student. On the first day of this year his seriousness for study was 1 hour. ...Read More »
• ### Sakib Knows The Number!

Ragib: I got digits of a 2 digit number Sakib: Is it an odd? Ragib: Yes. Moreover, the sum of ...Read More »
• ### Maths Genious Riddle

If u r genius solve it:- 40 * 14 = 11 30 * 13 = 12 20 * 12 = ...Read More »
• ### Calling 2 as 10 Riddle

When do we call “10” while looking at number “2”?Read More »