Google公司的考題... Exam Test From Google...

Q1:

1
11
21
1211
111221

請問...第六行是....?

What's the sixth row ?

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

第二題:

在下列數列中，接下來應該是甚麼數字:

What number comes next in the sequence:

10，9，60，90，70，66

A) 96
B) 1000000000000000000000000000000000\
0000000000000000000000000000000000\
000000000000000000000000000000000

C) Either of the above 以上接是
D) None of The Above 以上都不是

答看正不正確 我也不知道 ....

I am not sure the answer myself...

The sequence:

http://mathworld.wolfram.com/news/2004-10-13/google/

1
11
21
1211
111221
312211
13112221
1113213211
31131211131221

Solution: It's actually quite simple :) After starting the sequence with 1, each term in the sequence consists of groups of two numbers based on the previous term - the first being the quantity and the second specifying which digit.

Example: the first term is 1, which has "one 1" in it, therefore 11.
11 has "two 1's" in it, therefore 21.
21 has "one 2 and one 1" in it and therefore 1211.

This can be looked up and found to be sequence A052196 in the On-Line Encyclopedia of Integer Sequences, which gives the largest positive integer whose English name has n letters. For example, the first few terms are ten, nine, sixty, ninety, seventy, sixty-six, ninety-six, …. A more correct sequence might be ten, nine, sixty, googol, seventy, sixty-six, ninety-six, googolplex. And also note, incidentally, that the correct spelling of the mathematical term "googol" differs from the name of the company that made up this aptitude test.

The first few can be computed using the NumberName function in Eric Weisstein's MathWorld packages:

A mathematical solution could also be found by fitting a Lagrange interpolating polynomial to the six known terms and extrapolating:

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