brain teasers

1 There are 10 people in a room. Each person shakes hand with 3 other people, what is the total number of handshakes? A Note: we don’t care if person A shakes with B, C, D or E, F, G. But every person reaches out three times. Thus, the total number of hand reach-outs is $$10\ast 3=30$$ Every 2 reach-outs forms 1 handshake, thus total number of handshakes is 30 / 2 = 15.