Ruby, 1356 * 3 = 4068 bytes

if File.file?(?b)
s='P3
50 50
255
'
d=e=0
[153,44,6,1,42,1,6,1,42,1,6,1,42,1,6,1,42,1,6,1,42,1,6,1,42,1,4,40,5,1,4,1,1,1,36,1,5,1,4,1,1,1,36,1,5,1,4,1,1,1,36,1,5,1,4,1,1,1,36,1,5,1,4,1,1,34,3,1,5,1,4,1,34,1,3,1,5,1,4,1,34,1,3,1,5,1,4,1,34,1,3,1,5,1,4,1,34,1,3,1,5,1,4,1,34,1,3,1,5,1,4,1,34,1,3,1,5,1,4,1,34,1,3,1,5,1,4,1,34,1,3,1,5,1,4,1,34,1,3,1,5,1,4,1,34,1,3,1,5,1,4,1,34,1,3,1,5,1,4,1,34,1,3,1,5,1,4,1,8,31,5,1,4,1,8,1,25,1,9,1,4,1,8,1,25,1,9,1,4,1,8,1,25,1,9,1,4,1,8,1,25,1,9,1,4,1,8,1,25,1,9,1,4,1,8,1,25,1,9,1,4,1,8,1,25,1,9,1,4,1,8,37,4,1,34,1,14,1,34,1,14,1,34,1,14,1,34,1,14,1,34,1,14,1,34,1,14,1,34,1,14,1,34,1,14,1,34,1,14,1,34,1,14,1,34,1,14,36,63].map{|n|n.times{s+=[" 255 255 255"," 0 0 255"][d];s+=$/if (e+=1)%50==0};d=1-d}
File.write 'blue.ppm',s
elsif File.file?(?a)
puts "Mary had a little lamb,
Little lamb, little lamb,
Mary had a little lamb,
Its fleece was white as snow

And everywhere that Mary went,
Mary went, Mary went,
Everywhere that Mary went
The lamb was sure to go

It followed her to school one day
School one day, school one day
It followed her to school one day
Which was against the rules.

It made the children laugh and play,
Laugh and play, laugh and play,
It made the children laugh and play
To see a lamb at school"
`touch b`
else
1971.times{|i|$><<"#{i} "if i.to_s.chars.map(&:to_i).reduce(:+)%17<1}
`touch a`
end

I haven't golfed the second program yet. To keep track of the invocation, I'm creating an empty file a on the first run and an empty file b on the second run.

The first program uses a certain property of the numbers, and the third program currently uses just a naive run-length encoding. I'll look into actually encoding the path of the line later.

Ruby, 1356 1268 * 3 = 3804 bytes

if File.file?(?b)
s='P3
50 50
255
'
d=e=0
[153,44,6,1,42,1,6,1,42,1,6,1,42,1,6,1,42,1,6,1,42,1,6,1,42,1,4,40,5,1,4,1,1,1,36,1,5,1,4,1,1,1,36,1,5,1,4,1,1,1,36,1,5,1,4,1,1,1,36,1,5,1,4,1,1,34,3,1,5,1,4,1,34,1,3,1,5,1,4,1,34,1,3,1,5,1,4,1,34,1,3,1,5,1,4,1,34,1,3,1,5,1,4,1,34,1,3,1,5,1,4,1,34,1,3,1,5,1,4,1,34,1,3,1,5,1,4,1,34,1,3,1,5,1,4,1,34,1,3,1,5,1,4,1,34,1,3,1,5,1,4,1,34,1,3,1,5,1,4,1,34,1,3,1,5,1,4,1,8,31,5,1,4,1,8,1,25,1,9,1,4,1,8,1,25,1,9,1,4,1,8,1,25,1,9,1,4,1,8,1,25,1,9,1,4,1,8,1,25,1,9,1,4,1,8,1,25,1,9,1,4,1,8,1,25,1,9,1,4,1,8,37,4,1,34,1,14,1,34,1,14,1,34,1,14,1,34,1,14,1,34,1,14,1,34,1,14,1,34,1,14,1,34,1,14,1,34,1,14,1,34,1,14,1,34,1,14,36,63].map{|n|n.times{s+=[" 255 255 255"," 0 0 255"][d];s+=$/if (e+=1)%50==0};d=1-d}
File.write 'blue.ppm',s
elsif File.file?(?a)
puts [["","Mary had a ","little lamb",?,,?,,"Its fleece was white as snow"],["And ","everywhere that ","Mary went",?,,'',"The lamb was sure to go"],["","It followed her to ","school one day",'','',"Which was against the rules."],["","It made the children ","laugh and play",?,,'',"To see a lamb at school"]].map{|a,b,c,d,e,f|[a+b+c+d,c.capitalize+', '+c+d,b.capitalize+c+e,f]*$/}*"

"
`touch b`
else
1971.times{|i|$><<"#{i} "if i.to_s.chars.map(&:to_i).reduce(:+)%17<1}
`touch a`
end

To keep track of the invocation, I'm creating an empty file a on the first run and an empty file b on the second run.

• The first program uses a certain property of the numbers.
• The second program uses a bunch of reusable parts of the verses, but that currently only saves 100 bytes over naively printing the entire thing.
• The third program currently uses just a simple run-length encoding. I'll look into actually encoding the path of the line later.

The first program uses a certain property of the numbers, and the third program currently uses just a naive run-length encoding. I'll look into actually encoding the path of the line later.