Solutions to Chapter Problems

Chapter 20 Patterning and Algebraic Thinking

(p. 567):

190 handshakes. The first person shakes 19 hands; the next one 18 more hands; the next one 17 more hands; etc. The total number of handshakes is 1 + 2 +….. + 18 + 19.
Notice that  if 1 + 2 + …. + 18 + 19 is added to
            19+ 18 + ….  + 2  + 1
and the numbers are added vertically, there are 19 pairs of 20. This is twice as much as is desired, so the sum is 19 ×10, or 190.