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 Table Tennis Serve (Posted on 2013-07-17)
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 No Rating

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 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              247    15     9     6            15              226    14    10     7            17              205    13    11     8            19              184    12    12     9            21              163    11    13    10            23              142    10    14    11            25              121     9    15    12            27              100     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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