You could never guarantee 1000 handshakes because the people may choose not to shake hands!
If each person did shake hands with everyone else, then 46 people would suffice.
To absolutely guarantee that at least two people were born on the same date you would need 367 people. However with 29 people the odds would be approaching unity but it does not guarantee this will be the case.
1000*999/2 = 499500
1/2 of (29 x 28) = 29 x 14 = 406
Prison inmates.
28Good question. This is an 'analogue' of this puzzle: "Eight people meet for the first time. If they each shake hands with everyone else, how many handshakes are there?" There is a formula, but who would remember it?Imagine you and I are both among the eight people. You would shake hands with seven others. I would say the same thing, and so could each of the others.That gives 8x7 = 56, but you and I both counted the time we shook hands with one another , in fact each handshake is counted twice. The number of handshakes is actually 56/2 = 28.This can be generalized to say that the number of ways to choose 2 objects from a group of n objects is n(n-1)/2.
To absolutely guarantee that at least two people were born on the same date you would need 367 people. However with 29 people the odds would be approaching unity but it does not guarantee this will be the case.
If that happens you have to times ninexten and the answer would be 90 handshakes
200? D:
Everyone shakes hands with 4 other people. Since there are 5 people in the room this would suggest there are 5*4 = 20 handshakes. However, you would then be double counting handshakes: A shaking hands with B and B shaking hands with A is, in reality, only one handshake. Thus there are 5*4/2 = 10 handshakes in all.
6
there would be 26 handshakes if they were all done at once
i guarantee i will not die. The builder guarantees that his houses will be very strong, withstanding a flood !
1000*999/2 = 499500
1/2 of (29 x 28) = 29 x 14 = 406
that people would be able to elect their government
that people would be able to elect their government
I personally would not, but I guarantee there are people out there that would say yes.