數學問題集(45)---奇怪的數字

一位數學老師的朋友問他：「你教的那一班有多少人？」他回答：「有24名男生，32名女生，共100名學生。」已知這位老師的計算是無誤的，而且完全符合數學運算， 為甚麼會這樣的呢？

Ofcourse the teacher is right ...

because he don't use 10 進制 , he uses other . Use a 方程 to find what 進制 he uses

Let he uses a 進制 ,

( 2a + 4 ) + ( 3a + 2 ) = 1a^2

5a + 6 = a^2

a^2 - 5a - 6 = 0

( a - 6 ) ( a + 1 ) = 0

a = 6 or -1

Because there is no -1 進制 , so the teacher uses 6進制 .

--------------------------------------

Don't forget to CHECK :

{{ ( a ) = a進制 }}

24 ( 6 ) = 2 x 6 + 4 = 12 + 4 = 16 ( 10 )

32 ( 6 ) = 3 x 6 + 2 = 18 + 2 = 20 ( 10 )

100 ( 6 ) = 1 x 6^2 = 36 ( 10 )

16 ( 10 ) + 20 ( 10 ) = 36 ( 10 )

so , the teacher is right .

--------------------------------------

Why do we think the teacher is wrong ? It is because we think " 24 " , " 32 " , " 100 " these number is in 10進制 , but the question don't say these number is 10進制 or not , it makes us wrong . This is important .

--------------------------------------