Find the list of digits for squares of numbers less than 100 that contain successive repeated digits.

41.1

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In the first 100 Roman numerals, find those containing L, I and X in that order.

41.2

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Define a function f that tests whether a list of integers is the same as its reverse.

41.3

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Get a list of pairs of successive words in the Wikipedia article on alliteration that have identical first letters.

41.4

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Use Grid to show the sorting process in this section for {4,5,1,3,2}, with successive steps going down the page.

41.5

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Use ArrayPlot to show the sorting process in this section for a list of length 50, with successive steps going across the page.

41.6

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Start with 1.0, then repeatedly apply the “Newton’s method” function (#+2/# )/2& until the result no longer changes.

41.7

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Implement Euclid’s algorithm for GCD in which {a,b} is repeatedly replaced by {b,Mod[a,b]} until b is 0, and apply the algorithm to 12345, 54321.

41.8

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Define combinators using the rules s[x_][y_][z_]->x[z][y[z]],k[x_][y_]->x, then generate a list by starting with s[s][k][s[s[s]][s]][s] and applying these rules until nothing changes.

41.9

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Remove all trailing 0’s from the digit list for 100!.

41.10

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Start from {1,0} then for 200 steps repeatedly remove the first 2 elements, and append {0,1} if the first element is 1 and {1,0,0} if it is 0 and get a list of the lengths of the sequences produced (tag system).

41.11

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Start from {0,0} then for 200 steps repeatedly remove the first 2 elements, and append {2,1} if the first element is 0, {0} if the first element is 1, and {0,2,1,2} if it is 2, and make a line plot of the lengths of the sequences produced (tag system).

41.12

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