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[EIWL] Solving Example 6.10 of the Stephen Wolfram book

D P
Posted 9 years ago

Hi all.

I am working my way through the exercises on this page:

https://www.wolfram.com/language/elementary-introduction/06-making-tables.html

However I am stuck on Q. 6.10: Make a list line plot of the first digits of the first 100 squares.

IntegerDigits[Range[100]^2]

results in:

    {{1},{4},{9},{1,6},{2,5},{3,6},{4,9},{6,4},{8,1},{1,0,0},{1,2,1},{1,4,4},{1,6,9},{1,9,6},{2,2,5},{2,5,6},{2,8,9},{3,2,4},{3,6,1},{4,0,0},{4,4,1},{4,8,4},{5,2,9},

{5,7,6},{6,2,5},{6,7,6},{7,2,9},{7,8,4},{8,4,1},{9,0,0},{9,6,1},{1,0,2,4},{1,0,8,9},{1,1,5,6},{1,2,2,5},{1,2,9,6},{1,3,6,9},{1,4,4,4},{1,5,2,1},{1,6,0,0},{1,6,8,1},

{1,7,6,4},{1,8,4,9},{1,9,3,6},{2,0,2,5},{2,1,1,6},{2,2,0,9},{2,3,0,4},{2,4,0,1},{2,5,0,0},{2,6,0,1},{2,7,0,4},{2,8,0,9},{2,9,1,6},{3,0,2,5},{3,1,3,6},{3,2,4,9},

{3,3,6,4},{3,4,8,1},{3,6,0,0},{3,7,2,1},{3,8,4,4},{3,9,6,9},{4,0,9,6},{4,2,2,5},{4,3,5,6},{4,4,8,9},{4,6,2,4},{4,7,6,1},{4,9,0,0},{5,0,4,1},{5,1,8,4},{5,3,2,9},

{5,4,7,6},{5,6,2,5},{5,7,7,6},{5,9,2,9},{6,0,8,4},{6,2,4,1},{6,4,0,0},{6,5,6,1},{6,7,2,4},{6,8,8,9},{7,0,5,6},{7,2,2,5},{7,3,9,6},{7,5,6,9},{7,7,4,4},{7,9,2,1},

{8,1,0,0},{8,2,8,1},{8,4,6,4},{8,6,4,9},{8,8,3,6},{9,0,2,5},{9,2,1,6},{9,4,0,9},{9,6,0,4},{9,8,0,1},{1,0,0,0,0}}

Now I would like to count the length of individual elements in the above list ie. {1,1,1,2,2,2,2,2,2,3,3,3....}. But how?

Thanks in advance.

D

EDIT: This is not homework. I am self-learning Mathematica, and will be doing all the exercises in all 47 Chapters, which will probably take me a few weeks to a few months. Hence you may see me asking lots of questions in this forum! :)
POSTED BY: D P
18 Replies
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Other variations on the same subject of Exercise 6.10:

ListLinePlot[IntegerDigits[Range[100]^2][[;; , 1]]]
IntegerDigits[Range[100]^2][[;; , 1]] // ListLinePlot    
ListLinePlot[First /@ IntegerDigits[Range[100]^2]]
First /@ IntegerDigits[Range[100]^2] // ListLinePlot
Table[IntegerDigits[i^2][[1]], {i, 100}] // ListLinePlot
POSTED BY: Valeriu Ungureanu

A solution without Table[]:

ListLinePlot[IntegerDigits[Range[100]^2][[All, 1]]]
POSTED BY: Valeriu Ungureanu

That's interesting. I didn't understand at first how this could work, but 

IntegerDigits[Range[100]^2] // TableForm

makes it clear. From all rows, select the first column.
POSTED BY: Arno Bosse

From each row, select the first element.
POSTED BY: Valeriu Ungureanu
Jawad Mansoor
Jawad Mansoor
Posted 9 years ago

Thank you for in-depth answer above, however, I did not know syntax you used {embedded table formula and use of @ and in this example, this reply, /@. I found Arno Bosse's answer easier. (maybe because that was the solution I came upon first).

By the way, I am stuck at Question 8 of same chapter of the book. Any help?
POSTED BY: Jawad Mansoor
D P
D P
Posted 9 years ago

Scroll down all the way in the left pane, past the last chapter and there is a link to all the solutions.

I wonder how many people gave up on EIWL because they couldn't solve the problems and didn't see the solutions buried at the bottom(off screen).
POSTED BY: D P

About the notation @. It is so named prefix form, i.e. you may use notation f[x] or f@x. They are identical.

For example:

Plot[Sin[x], {x, -7, 7}]

is identical to:

Plot[Sin@x, {x, -7, 7}],

i.e. Sin[x] and **Sin@x** are identical.

About the notation /@. It stands for the function Map[].

For example, you can write:

In[1]:= Map[f, {a, b, c, d, e}]

Out[1]= {f[a], f[b], f[c], f[d], f[e]}

    or in alternative input form:

In[2]:= f /@ {a, b, c, d, e}

Out[2]= {f[a], f[b], f[c], f[d], f[e]}

P.S. The first solution without the symbol @ is equivalent to

ListLinePlot[
 Table[First[Part[IntegerDigits[Table[i^2, {i, 100}]], j]], {j, 100}]]
POSTED BY: Valeriu Ungureanu

About Exercise 6.8:

Make a list line plot of the number of digits in each of the first 100 squares.

One of the possible solutions:

ListLinePlot[Table[Length[IntegerDigits[i^2]], {i, 1, 100}]]

enter image description here

Another solution:

ListLinePlot[
 Table[Length[IntegerDigits[Range[100]^2][[i]]], {i, 100}]]

enter image description here
POSTED BY: Valeriu Ungureanu

Thank you, I was also very stuck on this one.
POSTED BY: Camille Driscoll
POSTED BY: Arno Bosse

Nice solution!
POSTED BY: Valeriu Ungureanu
POSTED BY: Valeriu Ungureanu

Dear D. P.,

I think that the title of your post must be changed as it doesn't reflect the essence of your question. It must be somewhat appropriate of this:

Solving Example 6.10 of the S. Wolfram book
POSTED BY: Valeriu Ungureanu
POSTED BY: Valeriu Ungureanu
D P
D P
Posted 9 years ago
POSTED BY: D P

I would use Table and Length like this:

list = IntegerDigits[Range[100]^2];
Table[Length[list[[i]]], {i, 1, Length[list]}]

I'm sure that there are other ways, but this one is pretty straightforward.
POSTED BY: Tim Mayes
Bill Simpson
Bill Simpson
Posted 9 years ago

Hint (and only a hint):

You have a list of items and you want to do the same thing to every one of those items.

Think "Map" and then think what is that thing that you want to do to every one of those individual items (which just happen to be lists).
POSTED BY: Bill Simpson
D P
D P
Posted 9 years ago
POSTED BY: D P
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