data/explorations/protractor_test_1.yaml - develop - githubmirror/oppia

data/explorations/protractor_test_1.yaml
1 034 строки35 KB
Kevin Thomas
Introduce edits_allowed property (#15396)
04 май 2022, 01:14
04 май 2022, 01:140d3d9c6
author_notes: ''
auto_tts_enabled: true
blurb: ''
category: Mathematics
correctness_feedback_enabled: false
edits_allowed: true
init_state_name: Intro
language_code: en
objective: learn how to count permutations accurately and systematically
param_changes: []
param_specs:
  guess:
    obj_type: UnicodeString
schema_version: 47
states:
  END:
    classifier_model_id: null
    content:
      content_id: content
      html: <p>Congratulations, you have finished!</p>
    interaction:
      answer_groups: []
      confirmed_unclassified_answers: []
      customization_args:
        recommendedExplorationIds:
          value: []
      default_outcome: null
      hints: []
      id: EndExploration
      solution: null
    next_content_id_index: 0
    param_changes: []
    recorded_voiceovers:
      voiceovers_mapping:
        content: {}
    solicit_answer_details: false
    written_translations:
      translations_mapping:
        content: {}
  Final challenge:
    classifier_model_id: null
    content:
      content_id: content
      html: '<p>Now here''s a final challenge: using what you''ve learned, can you
        figure out how many ways there are to arrange four balls in a row? Listing
        all the possibilities by hand is going to be tedious, but, by now, you''ve
        learned at least one way to calculate this number quickly and accurately.</p>'
    interaction:
      answer_groups:
      - outcome:
          dest: END
          feedback:
            content_id: feedback_1
            html: '<p>Yes, that is correct: the answer is 4 times the number of ways
              to arrange three balls in a row, so it is 4 times 6, which is 24! Well
              done.</p>'
          labelled_as_correct: false
          missing_prerequisite_skill_id: null
          param_changes: []
          refresher_exploration_id: null
        rule_specs:
        - inputs:
            x: 24.0
          rule_type: Equals
        tagged_skill_misconception_id: null
        training_data: []
      - outcome:
          dest: Final challenge
          feedback:
            content_id: feedback_2
            html: <p>Ahem. That, I think, is a trick answer, surely? I am pretty sure
              there's at least one way to arrange four balls in a line...</p>
          labelled_as_correct: false
          missing_prerequisite_skill_id: null
          param_changes: []
          refresher_exploration_id: null
        rule_specs:
        - inputs:
            x: 0.0
          rule_type: IsLessThanOrEqualTo
        tagged_skill_misconception_id: null
        training_data: []
      - outcome:
          dest: Final challenge
          feedback:
            content_id: feedback_3
            html: '<p>Hmm, that''s close-ish, but not quite. It feels like you may
              not have found all the possible cases. It''s really quite easy to miss
              some of them.


              You''re close to solving this, though. There''s an easy way and a hard
              way. The easy way is to use the reasoning we''ve developed previously
              to calculate the answer with a single multiplication. The hard way is
              to systematically find all the cases, and make sure that you haven''t
              missed any. It''s up to you whichever you pick, but you need to get
              an accurate answer!</p>'
          labelled_as_correct: false
          missing_prerequisite_skill_id: null
          param_changes: []
          refresher_exploration_id: null
        rule_specs:
        - inputs:
            a: 18.0
            b: 23.0
          rule_type: IsInclusivelyBetween
        tagged_skill_misconception_id: null
        training_data: []
      - outcome:
          dest: Final challenge
          feedback:
            content_id: feedback_4
            html: '<p>I think you''ve overcounted. This is quite common in counting
              problems, especially if you aren''t working systematically, or aren''t
              explicitly listing the things you''re counting.


              If you''re working from a list of possibilities, check it to make sure
              you have no duplicates! And you might also consider using the approach
              we''ve developed earlier in the exploration -- it''s much easier, and
              less prone to errors.</p>'
          labelled_as_correct: false
          missing_prerequisite_skill_id: null
          param_changes: []
          refresher_exploration_id: null
        rule_specs:
        - inputs:
            x: 24.0
          rule_type: IsGreaterThan
        tagged_skill_misconception_id: null
        training_data: []
      confirmed_unclassified_answers: []
      customization_args: {}
      default_outcome:
        dest: Final challenge
        feedback:
          content_id: default_outcome
          html: <p>Hmm, I don't think so, there are quite a lot more than that. Check
            your work, and try again.</p>
        labelled_as_correct: false
        missing_prerequisite_skill_id: null
        param_changes: []
        refresher_exploration_id: null
      hints: []
      id: NumericInput
      solution: null
    next_content_id_index: 5
    param_changes: []
    recorded_voiceovers:
      voiceovers_mapping:
        content: {}
        default_outcome: {}
        feedback_1: {}
        feedback_2: {}
        feedback_3: {}
        feedback_4: {}
    solicit_answer_details: false
    written_translations:
      translations_mapping:
        content: {}
        default_outcome: {}
        feedback_1: {}
        feedback_2: {}
        feedback_3: {}
        feedback_4: {}
  Found all the ways:
    classifier_model_id: null
    content:
      content_id: content
      html: <p>So, you've found that there are six ways to arrange these three balls.<br><br>Is
        that the same as your first guess?</p>
    interaction:
      answer_groups:
      - outcome:
          dest: Introspection
          feedback:
            content_id: feedback_1
            html: <p>Was it? I think you guessed {{guess}}, but there were actually
              6 ways.</p>
          labelled_as_correct: false
          missing_prerequisite_skill_id: null
          param_changes: []
          refresher_exploration_id: null
        rule_specs:
        - inputs:
            x: 0
          rule_type: Equals
        tagged_skill_misconception_id: null
        training_data: []
      - outcome:
          dest: Introspection
          feedback:
            content_id: feedback_2
            html: <p>Yes, you thought the number of ways was {{guess}}, but it was
              actually 6.</p>
          labelled_as_correct: false
          missing_prerequisite_skill_id: null
          param_changes: []
          refresher_exploration_id: null
        rule_specs:
        - inputs:
            x: 1
          rule_type: Equals
        tagged_skill_misconception_id: null
        training_data: []
      confirmed_unclassified_answers: []
      customization_args:
        choices:
          value:
          - content_id: ca_choices_3
            html: <p>Yes</p>
          - content_id: ca_choices_4
            html: <p>No</p>
        showChoicesInShuffledOrder:
          value: false
      default_outcome:
        dest: Introspection
        feedback:
          content_id: default_outcome
          html: ''
        labelled_as_correct: false
        missing_prerequisite_skill_id: null
        param_changes: []
        refresher_exploration_id: null
      hints: []
      id: MultipleChoiceInput
      solution: null
    next_content_id_index: 5
    param_changes: []
    recorded_voiceovers:
      voiceovers_mapping:
        ca_choices_3: {}
        ca_choices_4: {}
        content: {}
        default_outcome: {}
        feedback_1: {}
        feedback_2: {}
    solicit_answer_details: false
    written_translations:
      translations_mapping:
        ca_choices_3: {}
        ca_choices_4: {}
        content: {}
        default_outcome: {}
        feedback_1: {}
        feedback_2: {}
  General Theory:
    classifier_model_id: null
    content:
      content_id: content
      html: "<p>So: <br><br>There is 1 way to arrange 1 ball.<br>There are 2 ways\
        \ to arrange 2 balls.<br>There are\xC2\_6 ways to arrange 3 balls.<br><br>Let's\
        \ give these names. We will say F1 = 1, F2 = 2, F3 = 6. So, if you have n\
        \ balls (where n is 1, 2, 3, ...), then Fn is the number of ways to arrange\
        \ them.<br><br>Can you see a pattern here, or a systematic way to count them?\
        \ Let's have a look at the 3-ball case.<br><br>--------------------------------------------------------------------------------------------<br><br>First\
        \ you pick the ball on the left. This could be red, blue or yellow. There\
        \ are three cases to consider:<br><br>If the first ball is red, then there\
        \ are two balls left to arrange in the other two slots. And there are F2 ways\
        \ to do this.<br>If the first ball is blue, then there are two balls left\
        \ to ... hey, this is the same thing, it's just F2.<br>And, if the first ball\
        \ is yellow, then ... yada, yada, F2.<br><br>So the total number of ways to\
        \ arrange 3 balls, F3, is equal to 3 * F2. And all this works out correctly,\
        \ because F2 = 2, and F3 = 3 * 2 = 6.<br><br>--------------------------------------------------------------------------------------------<br><br>Now,\
        \ can you write out a similar expression for F2, in terms of F1? Then we'll\
        \ move on to figuring out F4, which starts to become hard to compute manually.</p>"
    interaction:
      answer_groups:
      - outcome:
          dest: Final challenge
          feedback:
            content_id: feedback_1
            html: <p>Yes! F2 = 2 * F1, since there are two ways to pick the ball on
              the left, and  for each of these 2 ways, there are F1 ways to arrange
              the other balls.</p>
          labelled_as_correct: false
          missing_prerequisite_skill_id: null
          param_changes: []
          refresher_exploration_id: null
        rule_specs:
        - inputs:
            x:
              contentId: rule_input_7
              normalizedStrSet:
              - 2F1
          rule_type: Contains
        tagged_skill_misconception_id: null
        training_data: []
      - outcome:
          dest: Final challenge
          feedback:
            content_id: feedback_2
            html: <p>Yes! F2 = 2 * F1, since there are two ways to pick the ball on
              the left, and  for each of these 2 ways, there are F1 ways to arrange
              the other balls.</p>
          labelled_as_correct: false
          missing_prerequisite_skill_id: null
          param_changes: []
          refresher_exploration_id: null
        rule_specs:
        - inputs:
            x:
              contentId: rule_input_8
              normalizedStrSet:
              - 2*F1
          rule_type: Contains
        tagged_skill_misconception_id: null
        training_data: []
      - outcome:
          dest: Final challenge
          feedback:
            content_id: feedback_3
            html: <p>Yes! F2 = 2 * F1, since there are two ways to pick the ball on
              the left, and  for each of these 2 ways, there are F1 ways to arrange
              the other balls.</p>
          labelled_as_correct: false
          missing_prerequisite_skill_id: null
          param_changes: []
          refresher_exploration_id: null
        rule_specs:
        - inputs:
            x:
              contentId: rule_input_9
              normalizedStrSet:
              - F1*2
          rule_type: Contains
        tagged_skill_misconception_id: null
        training_data: []
      - outcome:
          dest: Final challenge
          feedback:
            content_id: feedback_4
            html: <p>Yes! F2 = 2 * F1, since there are two ways to pick the ball on
              the left, and  for each of these 2 ways, there are F1 ways to arrange
              the other balls.</p>
          labelled_as_correct: false
          missing_prerequisite_skill_id: null
          param_changes: []
          refresher_exploration_id: null
        rule_specs:
        - inputs:
            x:
              contentId: rule_input_10
              normalizedStrSet:
              - 2 * F1
          rule_type: Contains
        tagged_skill_misconception_id: null
        training_data: []
      - outcome:
          dest: Final challenge
          feedback:
            content_id: feedback_5
            html: <p>Yes! F2 = 2 * F1, since there are two ways to pick the ball on
              the left, and  for each of these 2 ways, there are F1 ways to arrange
              the other balls.</p>
          labelled_as_correct: false
          missing_prerequisite_skill_id: null
          param_changes: []
          refresher_exploration_id: null
        rule_specs:
        - inputs:
            x:
              contentId: rule_input_11
              normalizedStrSet:
              - F1 * 2
          rule_type: Contains
        tagged_skill_misconception_id: null
        training_data: []
      confirmed_unclassified_answers: []
      customization_args:
        placeholder:
          value:
            content_id: ca_placeholder_6
            unicode_str: Type your answer here.
        rows:
          value: 1
      default_outcome:
        dest: Final challenge
        feedback:
          content_id: default_outcome
          html: <p>Alas, I don't understand the answer you just typed. Was it something
            like F2 = 2 * F1? If so, you are correct! There are two ways to pick the
            first ball, and F1 ways to pick the second one. This all works out because
            F1 = 1, so F2 = 2 * 1 = 2.</p>
        labelled_as_correct: false
        missing_prerequisite_skill_id: null
        param_changes: []
        refresher_exploration_id: null
      hints: []
      id: TextInput
      solution: null
    next_content_id_index: 12
    param_changes: []
    recorded_voiceovers:
      voiceovers_mapping:
        ca_placeholder_6: {}
        content: {}
        default_outcome: {}
        feedback_1: {}
        feedback_2: {}
        feedback_3: {}
        feedback_4: {}
        feedback_5: {}
        rule_input_10: {}
        rule_input_11: {}
        rule_input_7: {}
        rule_input_8: {}
        rule_input_9: {}
    solicit_answer_details: false
    written_translations:
      translations_mapping:
        ca_placeholder_6: {}
        content: {}
        default_outcome: {}
        feedback_1: {}
        feedback_2: {}
        feedback_3: {}
        feedback_4: {}
        feedback_5: {}
        rule_input_10: {}
        rule_input_11: {}
        rule_input_7: {}
        rule_input_8: {}
        rule_input_9: {}
  Guess a generalization:
    classifier_model_id: null
    content:
      content_id: content
      html: '<p>Now, let''s think about what happens if we had different numbers of
        balls. We know that the answer for three balls is 6. What if we had four balls
        to arrange?<br><br>Here''s a possible idea: 3 times 2 is 6, so the answer
        for four balls must be 4 times 2, which is 8. Basically, we just multiply
        the number of balls by 2, and get the answer. We''ve already shown that it
        works for 3 balls; we can figure out exactly why later.<br><br>Do you believe
        this reasoning? Do you agree that there are exactly 8 ways to arrange four
        balls of different colours in a line?</p>'
    interaction:
      answer_groups:
      - outcome:
          dest: Two balls
          feedback:
            content_id: feedback_1
            html: <p>All right! We have an answer. We could check it, I guess, by
              listing all sequences of four balls. But let's do something easier;
              let's try it with just two.</p>
          labelled_as_correct: false
          missing_prerequisite_skill_id: null
          param_changes: []
          refresher_exploration_id: null
        rule_specs:
        - inputs:
            x: 0
          rule_type: Equals
        tagged_skill_misconception_id: null
        training_data: []
      confirmed_unclassified_answers: []
      customization_args:
        choices:
          value:
          - content_id: ca_choices_2
            html: <p>Yes! It's clearly 8.</p>
          - content_id: ca_choices_3
            html: <p>No, I don't think it's 8.</p>
        showChoicesInShuffledOrder:
          value: false
      default_outcome:
        dest: Two balls
        feedback:
          content_id: default_outcome
          html: ''
        labelled_as_correct: false
        missing_prerequisite_skill_id: null
        param_changes: []
        refresher_exploration_id: null
      hints: []
      id: MultipleChoiceInput
      solution: null
    next_content_id_index: 4
    param_changes: []
    recorded_voiceovers:
      voiceovers_mapping:
        ca_choices_2: {}
        ca_choices_3: {}
        content: {}
        default_outcome: {}
        feedback_1: {}
    solicit_answer_details: false
    written_translations:
      translations_mapping:
        ca_choices_2: {}
        ca_choices_3: {}
        content: {}
        default_outcome: {}
        feedback_1: {}
  Intro:
    classifier_model_id: null
    content:
      content_id: content
      html: '<p>Suppose you were given three balls: one red, one blue, and one yellow.
        How many ways are there to arrange them in a straight line?</p>'
    interaction:
      answer_groups:
      - outcome:
          dest: correct but why
          feedback:
            content_id: feedback_1
            html: ''
          labelled_as_correct: false
          missing_prerequisite_skill_id: null
          param_changes: []
          refresher_exploration_id: null
        rule_specs:
        - inputs:
            x: 6.0
          rule_type: Equals
        tagged_skill_misconception_id: null
        training_data: []
      - outcome:
          dest: Intro
          feedback:
            content_id: feedback_2
            html: <p>Surely there's at least one? For example, you might have the
              red ball on the left, the blue ball in the middle, and the yellow ball
              on the right. Now try and find a few more. How many different ways can
              you find, in total?</p>
          labelled_as_correct: false
          missing_prerequisite_skill_id: null
          param_changes: []
          refresher_exploration_id: null
        rule_specs:
        - inputs:
            x: 0.0
          rule_type: IsLessThanOrEqualTo
        tagged_skill_misconception_id: null
        training_data: []
      confirmed_unclassified_answers: []
      customization_args: {}
      default_outcome:
        dest: Not 6
        feedback:
          content_id: default_outcome
          html: ''
        labelled_as_correct: false
        missing_prerequisite_skill_id: null
        param_changes: []
        refresher_exploration_id: null
      hints: []
      id: NumericInput
      solution: null
    next_content_id_index: 3
    param_changes: []
    recorded_voiceovers:
      voiceovers_mapping:
        content: {}
        default_outcome: {}
        feedback_1: {}
        feedback_2: {}
    solicit_answer_details: false
    written_translations:
      translations_mapping:
        content: {}
        default_outcome: {}
        feedback_1: {}
        feedback_2: {}
  Introspection:
    classifier_model_id: null
    content:
      content_id: content
      html: "<p>Can you think a little bit about why your answer was different from\
        \ six? Did you count a particular arrangement twice, or did you miss one?<br><br>Making\
        \ sure that you've counted everything can be tricky! Two common mistakes are\
        \ counting one thing twice, and forgetting to count some of the things. These\
        \ can be overcome by counting systematically and doing sanity checks.<br><br>In\
        \ the next few explorations, we'll explore what it means to count systematically,\
        \ and we'll talk a little about sanity checks. But why don't you try and discover\
        \ some of these for yourself? Take\xC2\_a couple of minutes, and think a bit\
        \ about some checks you can make to ensure that you don't overcount or undercount\
        \ things, or a systematic way that you could have used to count the balls.\
        \ Write these down here -- you will probably want to refer to them in a future\
        \ exercise, and we'll show your jottings to you again at that point.</p>"
    interaction:
      answer_groups:
      - outcome:
          dest: Introspection
          feedback:
            content_id: feedback_1
            html: <p>Come on, surely you have something...</p>
          labelled_as_correct: false
          missing_prerequisite_skill_id: null
          param_changes: []
          refresher_exploration_id: null
        rule_specs:
        - inputs:
            x:
              contentId: rule_input_3
              normalizedStrSet:
              - ''
          rule_type: Equals
        tagged_skill_misconception_id: null
        training_data: []
      confirmed_unclassified_answers: []
      customization_args:
        placeholder:
          value:
            content_id: ca_placeholder_2
            unicode_str: Type your answer here.
        rows:
          value: 1
      default_outcome:
        dest: Guess a generalization
        feedback:
          content_id: default_outcome
          html: ''
        labelled_as_correct: false
        missing_prerequisite_skill_id: null
        param_changes: []
        refresher_exploration_id: null
      hints: []
      id: TextInput
      solution: null
    next_content_id_index: 4
    param_changes: []
    recorded_voiceovers:
      voiceovers_mapping:
        ca_placeholder_2: {}
        content: {}
        default_outcome: {}
        feedback_1: {}
        rule_input_3: {}
    solicit_answer_details: false
    written_translations:
      translations_mapping:
        ca_placeholder_2: {}
        content: {}
        default_outcome: {}
        feedback_1: {}
        rule_input_3: {}
  Not 6:
    classifier_model_id: null
    content:
      content_id: content
      html: "<p>OK, you found {{guess}} ways to do this. I'd be interested in seeing\
        \ what you came up with; could you list the different ways?\_Write them as\
        \ three-character words, like this:<br><br>\_ \_ \_RBY<br><br>This means:\
        \ put the red ball on the left, the blue ball in the middle, and the yellow\
        \ ball on the right. Can you list all the ways you found?<br><br>\_ \_\_</p>"
    interaction:
      answer_groups:
      - outcome:
          dest: Not 6
          feedback:
            content_id: feedback_1
            html: <p>At least one of your list elements seems to be wrong. Can you
              check and make sure that each of them is a three-letter uppercase string
              that contains only the letters 'B', 'R' and 'Y' once each?</p>
          labelled_as_correct: false
          missing_prerequisite_skill_id: null
          param_changes: []
          refresher_exploration_id: null
        rule_specs:
        - inputs:
            x:
              contentId: rule_input_7
              unicodeStrSet:
              - RYB
              - BRY
              - BYR
              - RBY
              - YRB
              - YBR
          rule_type: HasElementsNotIn
        tagged_skill_misconception_id: null
        training_data: []
      - outcome:
          dest: Not 6
          feedback:
            content_id: feedback_2
            html: <p>You seem to have missed some arrangements with the red ball on
              the left...</p>
          labelled_as_correct: false
          missing_prerequisite_skill_id: null
          param_changes: []
          refresher_exploration_id: null
        rule_specs:
        - inputs:
            x:
              contentId: rule_input_8
              unicodeStrSet:
              - RBY
              - RYB
          rule_type: OmitsElementsIn
        tagged_skill_misconception_id: null
        training_data: []
      - outcome:
          dest: Not 6
          feedback:
            content_id: feedback_3
            html: <p>I think you're missing some!</p>
          labelled_as_correct: false
          missing_prerequisite_skill_id: null
          param_changes: []
          refresher_exploration_id: null
        rule_specs:
        - inputs:
            x:
              contentId: rule_input_9
              unicodeStrSet:
              - YBR
              - YRB
          rule_type: OmitsElementsIn
        tagged_skill_misconception_id: null
        training_data: []
      - outcome:
          dest: Not 6
          feedback:
            content_id: feedback_4
            html: <p>Have you found all the arrangements with a blue ball on the left?</p>
          labelled_as_correct: false
          missing_prerequisite_skill_id: null
          param_changes: []
          refresher_exploration_id: null
        rule_specs:
        - inputs:
            x:
              contentId: rule_input_10
              unicodeStrSet:
              - BRY
              - BYR
          rule_type: OmitsElementsIn
        tagged_skill_misconception_id: null
        training_data: []
      - outcome:
          dest: Found all the ways
          feedback:
            content_id: feedback_5
            html: ''
          labelled_as_correct: false
          missing_prerequisite_skill_id: null
          param_changes: []
          refresher_exploration_id: null
        rule_specs:
        - inputs:
            x:
              contentId: rule_input_11
              unicodeStrSet:
              - <p>RYB</p>
              - <p>BRY</p>
              - <p>BYR</p>
              - <p>RBY</p>
              - <p>YRB</p>
              - <p>YBR</p>
          rule_type: Equals
        tagged_skill_misconception_id: null
        training_data: []
      confirmed_unclassified_answers: []
      customization_args:
        buttonText:
          value:
            content_id: ca_buttonText_6
            unicode_str: Add item
      default_outcome:
        dest: Not 6
        feedback:
          content_id: default_outcome
          html: <p>No, try again.</p>
        labelled_as_correct: false
        missing_prerequisite_skill_id: null
        param_changes: []
        refresher_exploration_id: null
      hints: []
      id: SetInput
      solution: null
    next_content_id_index: 12
    param_changes:
    - customization_args:
        parse_with_jinja: true
        value: '{{answer}}'
      generator_id: Copier
      name: guess
    recorded_voiceovers:
      voiceovers_mapping:
        ca_buttonText_6: {}
        content: {}
        default_outcome: {}
        feedback_1: {}
        feedback_2: {}
        feedback_3: {}
        feedback_4: {}
        feedback_5: {}
        rule_input_10: {}
        rule_input_11: {}
        rule_input_7: {}
        rule_input_8: {}
        rule_input_9: {}
    solicit_answer_details: false
    written_translations:
      translations_mapping:
        ca_buttonText_6: {}
        content: {}
        default_outcome: {}
        feedback_1: {}
        feedback_2: {}
        feedback_3: {}
        feedback_4: {}
        feedback_5: {}
        rule_input_10: {}
        rule_input_11: {}
        rule_input_7: {}
        rule_input_8: {}
        rule_input_9: {}
  Two balls:
    classifier_model_id: null
    content:
      content_id: content
      html: <p>Let's try to find (or validate) a general pattern by looking at small
        cases. We do this because it's easy to compute the answers for small cases
        by hand, and they give us data which we can use to try and figure out a more
        general pattern.<br><br>The most obvious small case is 1 ball! There's one
        way to arrange one ball in a line.<br><br>How about 2 balls? How many ways
        are there to arrange two balls, with different colours, in a line?</p>
    interaction:
      answer_groups:
      - outcome:
          dest: General Theory
          feedback:
            content_id: feedback_1
            html: <p>Yes! That is correct. If the balls are red and blue, either the
              red one comes first, or the blue one comes first. Once you've picked
              the first one, the other choice is fixed.</p>
          labelled_as_correct: false
          missing_prerequisite_skill_id: null
          param_changes: []
          refresher_exploration_id: null
        rule_specs:
        - inputs:
            x: 2.0
          rule_type: Equals
        tagged_skill_misconception_id: null
        training_data: []
      - outcome:
          dest: Two balls
          feedback:
            content_id: feedback_2
            html: '<p>Hm. Might you be thinking that, since the answer for 3 balls
              is 6, the answer for 2 balls must be 4, because you just multiply by
              2?


              If so, alas, you''ve fallen into a trap! Look carefully at the 1-ball
              case: the answer is not 1 x 2 = 2, it is just 1. So this ''multiply
              by 2'' idea is not correct. We should be careful to avoid drawing conclusions
              based on just a single case.


              Why not try again? How many ways are there to arrange two balls in a
              row?</p>'
          labelled_as_correct: false
          missing_prerequisite_skill_id: null
          param_changes: []
          refresher_exploration_id: null
        rule_specs:
        - inputs:
            x: 4.0
          rule_type: Equals
        tagged_skill_misconception_id: null
        training_data: []
      - outcome:
          dest: Two balls
          feedback:
            content_id: feedback_3
            html: <p>Nah, that can't be right :-) There's at least one way to arrange
              two balls in a row, isn't there?</p>
          labelled_as_correct: false
          missing_prerequisite_skill_id: null
          param_changes: []
          refresher_exploration_id: null
        rule_specs:
        - inputs:
            x: 0.0
          rule_type: IsLessThanOrEqualTo
        tagged_skill_misconception_id: null
        training_data: []
      - outcome:
          dest: Two balls
          feedback:
            content_id: feedback_4
            html: <p>There's at least one more way. Try swapping the balls?</p>
          labelled_as_correct: false
          missing_prerequisite_skill_id: null
          param_changes: []
          refresher_exploration_id: null
        rule_specs:
        - inputs:
            x: 1.0
          rule_type: Equals
        tagged_skill_misconception_id: null
        training_data: []
      confirmed_unclassified_answers: []
      customization_args: {}
      default_outcome:
        dest: Two balls
        feedback:
          content_id: default_outcome
          html: <p>I think you may have counted something too many times. Try to remember
            the systematic approach you came up with earlier, and use it here...</p>
        labelled_as_correct: false
        missing_prerequisite_skill_id: null
        param_changes: []
        refresher_exploration_id: null
      hints: []
      id: NumericInput
      solution: null
    next_content_id_index: 5
    param_changes: []
    recorded_voiceovers:
      voiceovers_mapping:
        content: {}
        default_outcome: {}
        feedback_1: {}
        feedback_2: {}
        feedback_3: {}
        feedback_4: {}
    solicit_answer_details: false
    written_translations:
      translations_mapping:
        content: {}
        default_outcome: {}
        feedback_1: {}
        feedback_2: {}
        feedback_3: {}
        feedback_4: {}
  correct but why:
    classifier_model_id: null
    content:
      content_id: content
      html: <p>Right! Why do you think it is 6?</p>
    interaction:
      answer_groups:
      - outcome:
          dest: END
          feedback:
            content_id: feedback_1
            html: <p>Yes, the question is asking for the number of permutations of
              3 different balls, and that is 3! = 3 x 2 x 1. You can think about this
              by noticing that there are 3 ways to pick the first ball -- then, once
              you've done that, there are 2 ways to pick the second, and the last
              choice is forced. That's 3 x 2 = 6 ways.</p>
          labelled_as_correct: false
          missing_prerequisite_skill_id: null
          param_changes: []
          refresher_exploration_id: null
        rule_specs:
        - inputs:
            x:
              contentId: rule_input_4
              normalizedStrSet:
              - permutation
          rule_type: Contains
        tagged_skill_misconception_id: null
        training_data: []
      - outcome:
          dest: END
          feedback:
            content_id: feedback_2
            html: <p>Yes, the question is asking for the number of permutations of
              3 different balls, and that is 3 factorial, or 3 x 2 x 1. You can think
              about this by noticing that there are 3 ways to pick the first ball
              -- then, once you've done that, there are 2 ways to pick the second,
              and the last choice is forced. That's 3 x 2 = 6 ways.</p>
          labelled_as_correct: false
          missing_prerequisite_skill_id: null
          param_changes: []
          refresher_exploration_id: null
        rule_specs:
        - inputs:
            x:
              contentId: rule_input_5
              normalizedStrSet:
              - factorial
          rule_type: Contains
        tagged_skill_misconception_id: null
        training_data: []
      confirmed_unclassified_answers: []
      customization_args:
        placeholder:
          value:
            content_id: ca_placeholder_3
            unicode_str: Type your answer here.
        rows:
          value: 5
      default_outcome:
        dest: correct but why
        feedback:
          content_id: default_outcome
          html: '<p>OK! There are indeed 6 ways to arrange the balls: there are 3
            ways to choose the leftmost one, and for each of these, there are 2 ways
            to choose the second one; the last choice is then forced. This gives 3
            x 2 = 6 scenarios.


            If you do a quick search for the words ''permutation'' or ''factorial''
            on the Internet, you''ll also be able to find more information about this
            topic. See if you can figure out what the answer for 4 balls is!</p>'
        labelled_as_correct: false
        missing_prerequisite_skill_id: null
        param_changes: []
        refresher_exploration_id: null
      hints: []
      id: TextInput
      solution: null
    next_content_id_index: 6
    param_changes: []
    recorded_voiceovers:
      voiceovers_mapping:
        ca_placeholder_3: {}
        content: {}
        default_outcome: {}
        feedback_1: {}
        feedback_2: {}
        rule_input_4: {}
        rule_input_5: {}
    solicit_answer_details: false
    written_translations:
      translations_mapping:
        ca_placeholder_3: {}
        content: {}
        default_outcome: {}
        feedback_1: {}
        feedback_2: {}
        rule_input_4: {}
        rule_input_5: {}
states_schema_version: 42
tags: []
title: Protractor Test