In a game of table tennis, 24 of the 37 points played were won by the player serving, and Smith beat Jones 21-16. Remembering in table tennis that service alternates every five points, who served first?
S is Smith's points on serve and s when Jones was serving.
J is Jones's points on serve and j when Smith was serving.
S + s = 21 (1)
J + j = 16 (2)
S + J = 24 (3)
s + j = 13 (4)
S - j = 8 (1,4) (5)
Points scored on:
j S J s Jones's serve Smith's serve
--------------------- -----------------------------
8 16 8 5 13 24
7 15 9 6 15 22
6 14 10 7 17 20
5 13 11 8 19 18
4 12 12 9 21 16
3 11 13 10 23 14
2 10 14 11 25 12
1 9 15 12 27 10
0 8 16 13 29 8
Since service changes every 5 points, what is needed is one person serving 20 times and the other 17. Therefore Smith served 20 times and Jones 17, so Smith served first.
|
|
Posted by Charlie
on 2013-07-17 12:45:38 |
solution
