students.rb

# this requires ruby 2.3

students = {
  :"bobby crimble" => {
    math: 68,
    physics: 77,
    phys_ed: 81,
    english: 71
  },
  :"anne shirley" => {
    math: 69,
    physics: 76,
    phys_ed: 99,
    english: 87
  }
}

# transform students to:
# [
#   { math: "anne shirley" },
#   { physics: "bobby crimble" },
#   { phys_ed: "anne shirley" },
#   { english: "anne shirley" }
# ]

top_student_for_subject = {} # intermediate hash to accumulate highest grade and name for a subject
students.each do |name, report|
  report.each do |subject, grade|
    top_grade = top_student_for_subject.dig(subject, :grade) || 0
    top_student_for_subject[subject] = { name: name, grade: grade } if grade > top_grade
  end
end

subjects = [] # the final array of hashes
top_student_for_subject.each do |subject, student|
  subjects << { subject => student[:name] }
end

puts subjects