在一間酒吧，所有人互相碰杯，一共碰45次杯。
問：共有多少人在這酒吧？
數學問題 --- 推斷人數
2010-11-25 4:01 am
回答 (3)
2010-11-25 4:14 am
✔ 最佳答案
設有 n 人在酒吧 :每人都和另外 n - 1 人碰杯一次 , 所以 n 人碰杯共 n(n - 1) 次 , 但每次碰杯關乎兩人 , 實際是 n(n - 1)/2 次。n(n - 1)/2 = 45n(n - 1) = 90n^2 - n - 90 = 0(n - 10)(n + 9) = 0n = 10 或 n = - 9(捨去)這酒吧共 10 人。
2010-11-26 12:42 am
Use the concept of Factorials to answer:
Let there are n persons.
Set nC2 = 45,
we have n( n - 1 )/2 = 45
and consequently n^2 - n - 90 = 0
( n + 9 )( n - 10 ) = 0
n = 9 ( rej. for n > 0 ) and n = 10
A total of 10 persons are there.
Let there are n persons.
Set nC2 = 45,
we have n( n - 1 )/2 = 45
and consequently n^2 - n - 90 = 0
( n + 9 )( n - 10 ) = 0
n = 9 ( rej. for n > 0 ) and n = 10
A total of 10 persons are there.
參考: Mathematics Teacher Mr. Ip
2010-11-25 4:23 am
Very Nice!!
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