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Flow Chart

Six debutantes—Alison, Bridgette, Courtney, Dominique, Emily, Francine—meet at a party. During the time they have been at the party some girls have come to like certain other girls.
Amiable Alison likes every girl at the party.
Aloof, yet popular Bridgette likes no one at the party, but everyone likes her.
Courtney likes only two girls, one of whom is Dominique.
Dominique likes three girls, none of whom are Courtney or Francine.
Emily and Francine each like only one girl.

Alison likes every girl, so we start the “flow” with her:

Next, every girl likes Bridgette, but she does not like any of them. So we end the “flow” with Bridgette. (Note how the diagram evolves.)


Next, since Dominique likes three girls, two of whom are neither Courtney nor Francine, she must like both Alison and Emily, in addition to Bridgette. Adding this result plus the third condition, “Courtney likes Dominique,” to the diagram gives

Finally, since Emily and Francine each like only one girl and everyone likes Bridgette, Emily and Francine each must like Bridgette only. So there is nothing else to add to the diagram.


Note A,C,D forms a “loop”, because from A the arrows can be followed all the way around the “loop” back to A. But A,D,E does not form a loop, because from A you cannot get back to A, whether you go first to D, or first to E.
Of the following girls, who likes Emily?
I.   Alison
II.  Dominique
III. Francine
  1. I only
  2. II only
  3. III only
  4. I and II only
  5. I and III only
In the chart, only arrows from A and D point to E.
So only Alison and Dominique like Emily.
The answer is (D).
A “click” is a group of two or more girls who like one another. How many clicks are formed amongst the six girls?
  1. 0
  2. 1
  3. 2
  4. 3
  5. 4
There is only one. In the chart, a two-way arrow connects A and D, so they form a click.
The loop A,C,D does not form a click because it’s not two-way: A likes C, but that feeling is not reciprocal.
The answer is (B).
How many girls at the party like at least one girl whose feelings are not reciprocal?
  1. 2
  2. 3
  3. 4
  4. 5
  5. 6
In the chart, there are 5 arrows pointing to B, so 5 girls like B.
There are no arrows emanating from B, so none of those feelings are reciprocal.
The answer is (D).

Flow-chart games can bring to the fore some subtle issues, as the following difficult game illustrates.

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