Take the numbers 1 through 9, in order, and insert +'s and -'s (or nothing) such that the resulting mathematical expression evaluates to 100.

evalsto100.rb

#
# Recursively yield all possible expressions for the array of numbers
#
def exprs(nums)
  n, *rest = nums

  if rest.empty?
    yield "#{n}"
  else
    exprs(rest) do |expr|
      yield "#{n} + #{expr}"
      yield "#{n} - #{expr}"
      yield "#{n}#{expr}"
    end
  end
end
 
#
# Print out all expressions that evaluate to 100
# 
exprs([1, 2, 3, 4, 5, 6, 7, 8, 9]) do |expr|
  puts "#{expr} = 100" if eval(expr) == 100
end

Output:

1 + 23 - 4 + 56 + 7 + 8 + 9 = 100
12 + 3 - 4 + 5 + 67 + 8 + 9 = 100
1 + 2 + 34 - 5 + 67 - 8 + 9 = 100
1 + 2 + 3 - 4 + 5 + 6 + 78 + 9 = 100
123 - 4 - 5 - 6 - 7 + 8 - 9 = 100
123 + 45 - 67 + 8 - 9 = 100
1 + 23 - 4 + 5 + 6 + 78 - 9 = 100
12 - 3 - 4 + 5 - 6 + 7 + 89 = 100
12 + 3 + 4 + 5 - 6 - 7 + 89 = 100
123 - 45 - 67 + 89 = 100
123 + 4 - 5 + 67 - 89 = 100