為什麼會有不合邏輯思維,究竟點解呢

最後，住客每人各有１０元，共３０元，老闆有２５０元，服務生有２０元，加起來便是３００元。

這個謬誤出現的地方是「90X3+服務生的20元＝290」因為90x3是客人支出的錢，20是服務生拿到的錢。它們不是同一性質的，它們相加起來也是沒有意義的。

　

1) 老闆 receive $300.

2) 老闆 has $250 ; 服務生 has $50

3) 老闆 has $250 ; 服務生 has $20 ; 三個人 has $30

4) ($ owned by 老闆) + ($ owned by 服務生) = 250 + 20 = 270

5) ($ paid by 三個人) = 90 x 3 = 270
($ owned by 老闆 + $ owned by 服務生) = 250 + 20 = 270
So, ($ paid by 三個人) = ($ owned by 老闆 + $ owned by 服務生)
90 x 3 = 250 + 20

6) By equation in 5)
($ paid by 三個人) + ($ owned by 服務生)
= ($ owned by 老闆) + ($ owned by 服務生) + ($ owned by 服務生)
= ($ owned by 老闆) + 2 x ($ owned by 服務生)

7) But (ALL money) = $300 = ($ owned by 老闆) + ($ owned by 服務生)
+ ($ owned by 三個人) = $250 + $20 + $30

8) $ owned by 三個人 = 30
$ owned by 服務生 = 20
$ owned by 三個人 =\= $ owned by 服務生

9) Add the term [($ owned by 老闆) + ($ owned by 服務生)]
on both sides of the equation in 8), we obtain
[($ owned by 老闆) + ($ owned by 服務生)] + ($ owned by 服務生)
=\= [($ owned by 老闆) + ($ owned by 服務生)] + ($ owned by 三個人)

Substitute equation 5) into the equation above :
($ paid by 三個人) + ($ owned by 服務生)
=\= ($ owned by 老闆) + ($ owned by 服務生) + ($ owned by 三個人)
The equation above can be written as :
($ paid by 三個人) + ($ owned by 服務生) =\= (ALL $)

So, 270 + 20 =\= (ALL $)
[$ paid by 三個人 + $ owned by 服務生] does NOT equal to $300.
As a conclusion, it totally does NOT make any sense to
ask the question "90X3+服務生的20元＝290　那剩下的10元呢？？？"

2009-11-16 09:58:55 補充：
In fact,
90X3+服務生的20元 = ($ paid by 三個人) + ($ owned by 服務生)
Using equation 6):
($ paid by 三個人) + ($ owned by 服務生)
= [($ owned by 老闆) + ($ owned by 服務生)] + ($ owned by 服務生)
= ($ owned by 老闆) + 2 x ($ owned by 服務生)

2009-11-16 09:59:08 補充：
So, the physical meaning of 90X3+服務生的20元 is
90X3+服務生的20元
= ($ owned by 老闆) + 2 x ($ owned by 服務生)
= ($ owned by 老闆) + ($ owned by 服務生) + ($ owned by 服務生)

2009-11-16 09:59:12 補充：
This expression does NOT equal to (ALL $$$)
Instead, (ALL $$$) should be equal to :
(ALL $$$) = $300 = ($ owned by 老闆) + ($ owned by 服務生) + ($ owned by 三個人)

因為服務生想自己暗藏 20元起來，於是就把剩下的 30元還給他們,咁佢地就一共有
250+30=280
咁280除返3人...280/3=9.333333...係除唔進