A lot to sum up. I need everybody help.?

Question

Have you ever come across this question?

A boy was told by his teacher to sum up every number from 1 to 100. He gets the answer very quick. What is this formula all about? Please explain about it.

There are 100 people in a party. Everyone shake each other hand once. How many shaking hands took place in the entire party?

*** If A shake hands with B and C, B only needs to shake hands with C. C do not need to shake hands with neither A nor B.

Answer 1

The equation for summing any sets of number is known by many as Gauss law or equation. It states that the sum of any number from 1 to N is equal N(N+1)/2.

So what ever sets of number you wish to sum up just use the equation. Let us take your question.

The sum of 1 to 100 is = N(N+1)/2
100(100+1)/2 = 100(100+1)/2 = 10100/2 = 5050.

Now as with regard to your hand shake this is also a nice puzzle which can be calculate as follows:
First you have to acknowledge that the first one shakes hand with 99 not 100, the second with 98 .... the last one doesn't shake hand with any body..
The first person shakes hands with 99 people the second, with 98 the third with 97, the fourth, 96........ the 50th, with 50......the 60th with 40, the 80th with 20 ....the 90th with 10, the 95th with 5, and the 99th with only 1, and the last does not shake hand with any.

The equation to find out the number of hand shakes is N* (N-1)/2

So if you have 100 people in a party shaking hand one another, then the number of hand shakes is 100 times 99 divided by 2

H= 100(100-1)/2 =4950 hand shakes

Total hand shakes is equal to 100*99/2 which is equal to 9900/2. This is 4950 hand shakes all together.

Answer 2

I remember this problem form my college days. The answer is 5050 what the boy did to get the problem so quickly is to multiply 101 by 50. Now this is actually suposed to be a true story. I can't remember who the boy was but I think it was a famous composer like Mozart.

the first person shakes 99 hands the second person shakes 98 hands and so on. The answer is 4950. I cheated and used a spread sheet to get the answer but it is closely related to the first problem. incidently the answer 4950 = 99 * 50 not sure the of formula here.

Answer 3

I figured out the clever way to do this when I was a kid. (I wasn't the first -- Gauss did it when he was a little kid.) Imagine writing down the numbers 1 through 50 in a column. Just to the right, write the numbers 51 through 100, but in reverse order. The numbers in the first line are 1 and 100, total 101. The numbers in the second line are 2 and 99, total 101. Are you getting the picture? Fifty lines, each amounting to 101. So the total is 5050.

Answer 4

The second question is a bit like the first question:
1st person shakes 99 hands
2nd person shakes 98 hands
etc

Number of hands shaken:
99+ 98 + 97 + .... + 1 =
5050 - 100 = 4950

where I used the answer (5050) to the first question

Answer 5

summing was explained well.

As for the handshake, the first person needs to shake hands with 99 people. The second with 98 people, the third with 97, and so on. So all you have to do is sum up 1-99 using the same technique mentioned earlier.

Answer 6

Summing 1 to 100 is easy if you consider that 1+100=101, 2+99=101, etc. So just take 101*50 (50 of these pairs), and you get 5050

Answer 7

I know the first sum only..^_^

Okay, if we add the first and last numbers from 1 to 100.

1+100= 101

also, 2+99+101

also, 3+98=101.

See?? so, if you multiply 101 into 50 times, you get the answer...^_^

Hey wait, I also know the second answer.

If 100 ppl shake 100 ppl's hands then the answer is 100 x 100 =10000!!>.^_^

COOL!!

Come one dude, I deserve to be chosen as best answer...right??

COME ON!!

Click the "Choose As Best Answer" button!!...^_^

Answer 8

1) S=n(A1+An) / 2
n is the number of terms
A1 is the first term
An is the last term
S= 100(1+100) / 2=5050

2) add all the potion number from 1 to 99.
S= 99(1+99) / 2= 4950 handshakes

Answer 9

200 hands who knows

Answer 10

no clue i have an e in math moo hoo ha ha