Nine students from three local high schools met at the Apple Blossom Mall. Three students attended Sherando High School, three went to Millbrook, and three were Handley students.

Handley students always tell the truth.
Sherando students always lie.
Millbrook students utter a mixture of both lies and truth
(always at least one of each).

Each of the nine students has made three statements, each individual statement being either entirely true or entirely false.

Al made the following statements:
a1 I am a student at Handley.
a2 Hank is not a student at Handley.
a3 Isabel is a student at Handley.

Bonnie made the following statements:
b1 I am a student at Handley.
b2 Cal is not a student at Sherando.
b3 Gary is not a student at Handley.

Cal made the following statements:
c1 I am a student at Handley.
c2 Ellie is not a student at Handley.
c3 Hank is not a student at Millbrook.

Dana made the following statements:
d1 I am a student at Handley.
d2 Bonnie is a student at Millbrook.
d3 Gary is a student at Sherando.

Ellie made the following statements:
e1 I am a student at Handley.
e2 Dana is not a student at Handley.
e3 Al and Isabel are both students at Handley.

Fran made the following statements:
f1 I am a student at Handley.
f2 Gary is a student at Handley.
f3 Bonnie is not a student at Handley.

Gary made the following statements:
g1 I am a student at Handley.
g2 Fran is not a student at Millbrook.
g3 Hank is a student at the same school as I am.

Hank made the following statements:
h1 I am a student at Handley.
h2 Cal and Fran are not students at Sherando.
h3 Al is not a student at Handley.

Isabel made the following statements:
i1 I am a student at Handley.
i2 Dana is not a student at Millbrook.
i3 Cal is a student at Sherando.

Using these statements, can you determine which of these students attend Handley, which attend Sherando, and which attend Millbrook?


 

Solution to the Problem:

students at Handley: Cal, Dana, Hank.
students at Sherando: Al, Ellie, Gary.
students at Millbrook: Bonnie, Fran, Isabel.

This puzzle involves following hypothetical paths of truth to find those that hold up. One helpful fact is that all nine students say they're students at Handley, so six of them must be lying, and the other three must be truthful. You can start by figuring out which students can't be students at Handley - that is, can't be telling the whole truth.

One path to the truth is:
1) If Ellie goes to Handley, then Al and Isabel do too (statement e3), and thus must be the only other students at Handley. Isabel truthfully says that Dana isn't a student at Millbrook (i2), so Dana must be a student at Sherando. Dana lies that Bonnie is a student at Millbrook (d2), so Bonnie must be a student at Sherando. Bonnie lies that Gary is not a student at Handley (b3), but Gary must not be a student at Handley, because Ellie, Al, and Isabel already are. So Ellie can't be a student at Handley.

2) If Isabel is a student at Handley, then Cal is a student at Sherando (i3). But she lies that Ellie is not a student at Handley (c2). We know Ellie is not a student at Handley (above). So Isabel can't be a student at Handley.

3) Since Isabel can't be a student at Handley, Al can't truthfully say Isabel is (a3). So Al can't be a student at Handley.

4) If Fran is a student at Handley, then so is Gary (f2) and so is Hank (g3). Hank truthfully says that Cal is not a student at Sherando (h2), so since all at the Handley slots are full, Cal must be a student at Millbrook. Bonnie's right that Cal isn't a student at Sherando (b2), so Bonnie is a student at Millbrook. Dana's right that Bonnie is a student at Millbrook (d2), so Dana is too. Ellie's right that Dana isn't a student at Handley (e2), so Ellie is a student at Millbrook. But that's four students at Millbrook, and that's impossible. So Fran can't be a student at Handley.

5) If Gary is a student at Handley, then so is Hank (g3). Gary says that Fran isn't a student at Millbrook (g2), and Hank says Fran isn't a student at Sherando (h2), so since they're both truth-tellers, Fran must also be a student at Handley. But we know from paragraph 4 above that she isn't. So Gary can't be a student at Handley.

6) All four remaining students (Bonnie, Cal, Dana, and Hank) seem to be telling the truth, except that Dana says Bonnie is a student at Millbrook (d2). One at them must be lying, meaning that Cal and Hank must be students at Handley. Hank says Fran isn't a student at Sherando (h2), and we know Fran isn't a student at Handley, so she goes to Millbrook. Since by paragraph 5 above she is lying about Gary being a student at Handley, she must be telling the truth about something, namely that Bonnie is not a student at Handley. Now we know that Cal, Dana, and Hank are students at Handley, and Fran is a student at Millbrook. Dana confirms Gary is a student at Sherando (d3). Isabel's first and third statements are false, and her second is true, so she is a student at Millbrook. All three of both Ellie's and Al's statements have now been proven false, so they are students at Sherando.

In summary:
students at Handley: Cal, Dana, Hank.
students at Sherando: Al, Ellie, Gary.
students at Millbrook:
    Bonnie (b2 & b3 true),
    Fran (f3 true),
    Isabel (i2 true).

Correctly solved by:

1. David & Judy Dixon Bennettsville, South Carolina
2. Cameron Burkholder Winchester, Virginia
3. Emily Auerbach Columbus, Georgia
4. Tristan Collins Winchester, Virginia
5. Jeffrey Gaither Winchester, Virginia
6. Chris Rogers Winchester, Virginia