Problem 16
completed November 30, 2011Try One
Comments
The problem I’m having here is that the number 2^1000 is so large that the computer can’t handle it. The scripting program I’m using turns it into scientific notation and thus I can’t count the digits.
I am going to look to one of two options. First, looking for patterns in the sums and looking for more information on counting digit patterns. I know a pattern exists for 3, 6, and 9. So, feasibly there is also one for 2. Second, I will look at other scripting languages. I’m thinking one of them may be able to handle the larger output.
Resources
I pulled up Mathematica. It gave 2^1000 nicely.
Results
Well, looks like I’ll need a different scripting language. Gotta love Apple though for these finer touches.
Try Two
Resources
Okay. Goodbye Applescript. Hello Mathematica!
Comments
Well, that was easy.
Code
In[1]:= 2^1000
Out[1]= 10715086071862673209484250490600018105614048117055336074437503\
8837035105112493612249319837881569585812759467291755314682518714528569\
2314043598457757469857480393456777482423098542107460506237114187795418\
2153046474983581941267398767559165543946077062914571196477686542167660\
429831652624386837205668069376
In[2]:= characters[\
1071508607186267320948425049060001810561404811705533607443750388370351\
0511249361224931983788156958581275946729175531468251871452856923140435\
9845775746985748039345677748242309854210746050623711418779541821530464\
7498358194126739876755916554394607706291457119647768654216766042983165\
2624386837205668069376]
In[3]:= characters[\
"107150860718626732094842504906000181056140481170553360744375038837035\
1051124936122493198378815695858127594672917553146825187145285692314043\
5984577574698574803934567774824230985421074605062371141877954182153046\
4749835819412673987675591655439460770629145711964776865421676604298316\
52624386837205668069376"]
Out[3]= characters[\
"107150860718626732094842504906000181056140481170553360744375038837035\
1051124936122493198378815695858127594672917553146825187145285692314043\
5984577574698574803934567774824230985421074605062371141877954182153046\
4749835819412673987675591655439460770629145711964776865421676604298316\
52624386837205668069376"]
In[4]:= list = {1, 0, 7, 1, 5, 0, 8, 6, 0, 7, 1, 8, 6, 2, 6, 7, 3, 2,
0, 9, 4, 8, 4, 2, 5, 0, 4, 9, 0, 6, 0, 0, 0, 1, 8, 1, 0, 5, 6, 1,
4, 0, 4, 8, 1, 1, 7, 0, 5, 5, 3, 3, 6, 0, 7, 4, 4, 3, 7, 5, 0, 3,
8, 8, 3, 7, 0, 3, 5, 1, 0, 5, 1, 1, 2, 4, 9, 3, 6, 1, 2, 2, 4, 9,
3, 1, 9, 8, 3, 7, 8, 8, 1, 5, 6, 9, 5, 8, 5, 8, 1, 2, 7, 5, 9, 4,
6, 7, 2, 9, 1, 7, 5, 5, 3, 1, 4, 6, 8, 2, 5, 1, 8, 7, 1, 4, 5, 2,
8, 5, 6, 9, 2, 3, 1, 4, 0, 4, 3, 5, 9, 8, 4, 5, 7, 7, 5, 7, 4, 6,
9, 8, 5, 7, 4, 8, 0, 3, 9, 3, 4, 5, 6, 7, 7, 7, 4, 8, 2, 4, 2, 3,
0, 9, 8, 5, 4, 2, 1, 0, 7, 4, 6, 0, 5, 0, 6, 2, 3, 7, 1, 1, 4, 1,
8, 7, 7, 9, 5, 4, 1, 8, 2, 1, 5, 3, 0, 4, 6, 4, 7, 4, 9, 8, 3, 5,
8, 1, 9, 4, 1, 2, 6, 7, 3, 9, 8, 7, 6, 7, 5, 5, 9, 1, 6, 5, 5, 4,
3, 9, 4, 6, 0, 7, 7, 0, 6, 2, 9, 1, 4, 5, 7, 1, 1, 9, 6, 4, 7, 7,
6, 8, 6, 5, 4, 2, 1, 6, 7, 6, 6, 0, 4, 2, 9, 8, 3, 1, 6, 5, 2, 6,
2, 4, 3, 8, 6, 8, 3, 7, 2, 0, 5, 6, 6, 8, 0, 6, 9, 3, 7, 6};
Total[list]
Out[5]=