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Table Tennis Serve (Posted on 2013-07-17) Difficulty: 3 of 5
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?

No Solution Yet Submitted by K Sengupta    
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Solution solution | Comment 2 of 6 |

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
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