simple question for you, but hard for me.. please help me!!!!!?

Question

ok here it is: in a room everyone shook hands. there was 23 people in this room. each person shook everyones hand once. how many handshakes were shook during this time? i got 506 because i multipled 23 x 22 to get 506. is this right? please help

Answer 1

Trentino is indeed correct.

Prove it to yourself with a smaller number of people as an example.

If there were 3 people in a room and they each shook hands once with every other person in the room how many would there be?

you 23x23, or 23x22 people would be saying that in this example the answer would be 3x3=9 or 3x2=6, but that would be wrong. Person 3 shakes the hands of persons 2 and 1=2 shakes, Then add the number of shakes that person 2 has to make... he already shook person 3's hand, so he only has to shake person 1's hand, = 1 hand shake.

So you have 2 shakes plus 1 shake for a total of 3 shakes. person one has no more to add because he has already shaken with persons 3 and 2. it's 3 shakes not 6 or 9...

For you non-believers, if you can add, you have..... 22+21+20+19+18+17+16+15+14+
13+12+11+10+9+
8+7+6+5+4+3+2+1=253

Answer 2

Look at it this way...the first guy shakes hands with 22 people. The second guy already shook the first guy's hand, so he only has to shake hands with 21 people. It helps if you think of them all standing in a line. The guy at the end goes down the line, shakes everyones hand, then leaves the room. Using this reasoning, you get:

22+21+20+19+...+1

You can either add all this by hand, or use the rule that when you add the numbers 1 through n, the answer is (n)(n+1)/2. In this case, that gives you (22)(23)/2, which equals 253.

Answer 3

Two ways to look at this:

1) there are 23 people and each shakes the hand of the other 22 and take 1/2 of that to account for double counts so:

Ans = 23*22/2 = 23 * 11 = 253 hand shakes.

OR

2) the first person shakes 22 other peoples' hands, the second person shakes 22 other peoples hands, but his/her interaction with the first person was already counted so to eliminate double counts, we only total 21, the third person only accounts for 20 handshakes and so on until the 22nd person only accounts for 1 hand shake to be added to the running total. In each case the persons position and countable handshakes adds up to a constant 23, the 12th person counts for 11 shakes, in each case the count is decreasing by one and is added to the total hand shake, so:
22+21+20+19........+3+2+1= 253
A simpler way to add this is to note that the first and last term add up to 23 so does the second and second to last, and the third and third to last, and so on. this happens 11 times, 1/2 the number of terms (22), so:
11*23 = 253 hand shakes.
the same operation we did in part 1.

Answer 4

No. The problem with the way you did it is that you counted (for example) when Suzie shook hands with Sam and when Sam shook hands with Suzie.

Try adding 22+21+20+19 . . . .

I did it assuming 5 people in the room to check it. It makes sense. (And, yeah, I know that you have 23 people--I started you on 22 intentionally). Make 5 x's. The first one shakes with the other four (4). The second one already shook with the first, so he shakes with the other three (3). The third one already shook with the first and second, so he shakes with the other two (2). The fourth one already shook with the first three, so he shakes with the other one (1). The fifth one has already shaken hands with everyone, so he's done. So add 4+3+2+1=10.

Answer 5

23 x 23 is wrong.

23 + 22 + 21 + 20 + 19 + 18 + 17 + 16 + 15 + 15 + 14 + 13 + 12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1


276.

Answer 6

Number of handshaking in n persons is
N = C(n, 2) = n(n -- 1)/2
In 23 persons, number of handshaking
= C(23, 2)/2
= 23x22/2
= 253 only not 506

Answer 7

i would say there are 23 people so each person shook 22 times
so 22 added 23 times is 506 but then divide it by 2
so 253 cuz it is dupicated

Answer 8

I think it would be 23 x 22 and then divide that by 2 because if you and I were in the room.....you shaking my hand would be the same as me shaking your hand....by calculating 23 x 22 you're counting us shaking hands as two different handshakes when that's not the case. Thus, it would be 253, hope this makes sense.

Answer 9

Correct answer is 253.
Person 1 does 22 handshakes.
Person 2 does 21 more handshakes; because he has already shaken with person 1. Person 3 does 20 more handshakes, because he has already shaken with person 1 & 2.
Keep going in this manner. When you get to person 23 he will have no new handshakes because everybody has already shaken with him.

Answer 10

The handshake problem appears all over the place. The formula to solve it is (n^2 - n)/2 where n = the number of people. In your problem you would set up (23^2 - 23)/2 and you should get 253.