There are a lot of approaches to solve Problem 6.10

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

But, we must use only the functions exposed in the first 6 chapters. So...

We can generate a list of the first 100 squares:

In[1]:= Table[i^2, {i, 100}]

Out[1]= {1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, \
225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, \
841, 900, 961, 1024, 1089, 1156, 1225, 1296, 1369, 1444, 1521, 1600, \
1681, 1764, 1849, 1936, 2025, 2116, 2209, 2304, 2401, 2500, 2601, \
2704, 2809, 2916, 3025, 3136, 3249, 3364, 3481, 3600, 3721, 3844, \
3969, 4096, 4225, 4356, 4489, 4624, 4761, 4900, 5041, 5184, 5329, \
5476, 5625, 5776, 5929, 6084, 6241, 6400, 6561, 6724, 6889, 7056, \
7225, 7396, 7569, 7744, 7921, 8100, 8281, 8464, 8649, 8836, 9025, \
9216, 9409, 9604, 9801, 10000}

In this list, we must find the digits of each number:

In[39]:= IntegerDigits@Table[i^2, {i, 100}]

Out[39]= {{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}}

We can generate a list of the first digits in each sub-list by different means. But, the beginner knows at this point only a few possibilities. First, we must identify every sub-list and its first element. For this, we use functions Part[] and First[]. Second, to generate a list, we use function Table[]:

In[43]:= Table[
 First@Part[IntegerDigits@Table[i^2, {i, 100}], j], {j, 100}]

Out[43]= {1, 4, 9, 1, 2, 3, 4, 6, 8, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 4, \
4, 4, 5, 5, 6, 6, 7, 7, 8, 9, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, \
1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, \
4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, \
8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 1}

And finally, we can use ListLinePlot[]:

ListLinePlot[
 Table[First@Part[IntegerDigits@Table[i^2, {i, 100}], j], {j, 100}]]

An equivalent code to the previous one:

ListLinePlot[
 Table[First[Part[IntegerDigits[Table[i^2, {i, 100}]], j]], {j, 100}]]

There are other elegant solutions of this problem, e.g.:

First /@ IntegerDigits@Table[i^2, {i, 100}] // ListLinePlot

But, the last code uses the function Map[] (/@) which is supposedly not known in Chapter 6 of the book.

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.

Thank you, I was also very stuck on this one.

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

From each row, select the first element.

A solution without Table[]:

ListLinePlot[IntegerDigits[Range[100]^2][[All, 1]]]

Hi Bill, thanks for your reply.

I think that I am expected to use functions that have been taught in the previous chapters ie. Table, Count, IntegerDigits, Length, Range. Map has not been taught yet.

Essentially, what I need to do is to Count the number of elements in each element of the list. I know that there are 100 elements in the list, each consisting of 1 or more elements.

So I need something like: Count[IntegerDigits[Table[n^2, {n, 100}]]] , which doesn't quite work. I strongly suspect the command is a combination of Count(or Length), IntegerDigits, Range, and perhaps Table.