binary number!!

2011-03-31 3:23 am
Here is a question:
Mr wong is x year old.He had 2 sisters,one is one year older than him,one is two year older than him.
The sum of their ages is represented by a binary number,each dight of the number is 1.

Help!!Please show the steps to find the answer.
更新1:

But the right answer is 86...I dont know how to get it..

更新2:

Mr wong is 86.

更新3:

So the answer is 84?Mr wong must not be 4 or 20 too young.

回答 (1)

2011-03-31 3:51 am
✔ 最佳答案
The sum of their ages = x + (x+1) + (x+2) = 3x + 3 is divisible by 3.111 111 111(2)
= 2^9 - 1
= 511 years old of the sum of 3 people ages is impossible. 11 111 111(2)
= 2^8 - 1
= 255 is possible but not divisible by 3.1 111 111(2)
= 2^7 - 1
= 127 is possible but not divisible by 3.111 111(2)
= 2^6 - 1
= 63 is divisible by 3.3x+3 = 63
x = 20
Mr wong is 20 years old.11 111(2)
= 2^5 - 1
= 31 is not divisible by 3.1111(2)
= 2^4 - 1
= 15 is divisible by 3.3x+3 = 15
x = 4
Mr wong is 4 years old.111(2)
= 7 is not divisible by 3.11(2)
= 3
3x+3 = 3
x = 0 (rejected).Mr wong is 4 or 20 years old.


2011-03-30 19:54:11 補充:
Missing one case :

11 111 111(2)
= 2^8 - 1
= 255 is possible ,

3x+3 = 255
x = 84

Mr wong is 4 or 20 or 84 years old.

2011-03-31 23:07:32 補充:
I think 86 is the ages of his big sister.

2011-04-01 14:18:03 補充:
If Mr wong is 86 , then his sisters is 87 and 88.

86 + 87 + 88

= 261 = 100 000 101(2)

NOT each dight of the number is 1.

So 86 is wrong.


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