Problem Statement

The Thue-Morse sequence is a sequence of ones and zeros that if two people take turns in the given order, the first persons turn for every '0' in the sequence, the second for every '1'; then this is shown to give a fairer, more equitable sharing of resources. (Football penalty shoot-outs for example, might not favour the team that goes first as much if the penalty takers take turns according to the Thue-Morse sequence and took 2^n penalties) The Thue-Morse sequence of ones-and-zeroes can be generated by:

Use this method:

Counting from zero;   using a function/method/routine to express an integer count in base b, sum the digits modulo b to produce the next member of the Thue-Morse fairshare series for b people.

Show the first 25 terms of the fairshare sequence:

Let's start with the solution:

proc fairshare(word n, base) word:
    word result;
    result := 0;
    while n>0 do
        result := result + n % base;
        n := n / base
    od;
    result % base
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proc main() void:
    [4]word bases = (2,3,5,11);
    word b, n;
    for b from 0 upto 3 do
        write(bases[b]:2, ':');
        for n from 0 upto 24 do
            write(fairshare(n, bases[b]):3)
        od;
        writeln()
    od
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