| By clue 7, no two bills received the same number of YES votes; the only way
for this to work would be if the votes were 5-0, 4-1, 3-2, 2-3, 1-4, and 0-5
YES/NO. Also by clue 7, no two council members voted YES the same number
of times. Since one bill passed unanimously and one bill was defeated
unanimously, no council member cast 6 YES votes or 6 NO votes; the only way
for clue 7 to work is if the five council members voted 5-1, 4-2, 3-3, 2-4,
and 1-5 YES/NO. Five of the bills are listed in clue 1. One bill is the
one defeated by a 2 YES/3 NO margin. A second bill is the one passed
unanimously, 5-0, and is the only bill which the council member who had a
1-5 YES/NO record voted to approve. The member with the 1-5 record thus
cast the only dissenting vote to the bill passed 4-1; in clue 1, then, since
Ian had a 2-4 YES/NO voting record, Ian had to have voted for the bills that
passed 5-0 and 4-1. So a third bill in clue 1 is the one that passed 4-1.
Since in clue 1 the bill to build a new library passed, it passed by a 3-2
margin and is therefore a fourth bill. Finally in clue 1, the fifth bill
got a YES vote from Bailey and thus must be the bill defeated by a 1-4 vote
The sixth bill is then the one unanimously defeated, 0-5. Since Ian had a 2-4
voting record and voted against all the bills except those passed 5-0 and 4-1,
Ian and Bailey are two different council members. By clue 3, John and Earhart cast
the only YES votes for the bill to ban smoking in all Summerset County parks. So,
the smoking bill is the one that lost by a 2-3 vote. Since Ian voted against
that bill, Ian isn't Earhart; Earhart is the third council member to Ian and
Bailey. Since Bailey is the only one who voted YES on the bill that lost 1-4,
Earhart voted NO on it; Earhart also voted NO on the bill that lost 0-5 and
YES on the bill passed 5-0. By clue 5, Helen and Angelico voted YES on the
bills to hire a new police chief and to approve the school budget; therefore,
those bills must be the ones passed 5-0 and 4-1 or vice versa. Since Kathy
voted NO on the new police chief (clue 6), it passed 4-1 and the school budget
passed unanimously. Since the bill to raise the height restriction on buildings
in Summerset County didn't get a unanimous vote (4), it lost 1-4, with the
bill to implement a county sales tax defeated unnanimously. Since all the
council members but Bailey voted NO on the bill that lost 1-4 and also voted
NO on the bill that was unanimously defeated, they must have cast at least
2 NO votes; Bailey thus must be the council member with the 5-1 YES/NO
voting record and thus voted for all the bills but the one that lost by
the 0-5 count. We know that since Bailey and Earhart cast the
only YES votes on the smoking ban and Bailey cast the only YES vote on the
height restriction, the fourth and fifth council members had to have voted
NO on both those bills as well as on the unanimously-defeated sales tax
proposal. Therefore, the fourth and fifth members made at most three YES
votes--and Earhart must be the member with the 4-2 YES/NO record, voting for
the new police chief and library. If we arbitrarily have the fourth council
member voting YES and the fifth voting NO on the police chief, then the
fourth council member must also have voted YES on the library or he/she
would have had the same 2-4 record as Ian. The fourth council member thus
had a 3-3 record. The fifth member voted NO on the library and had a 1-5
record. Since the fifth member is the only one who voted against naming
the new police chief, she is Kathy in clue 6. By clue 3, John is Bailey.
Kathy isn't Angelico (5); nor can she be Dickey in clue 2; she is Cohen.
If Gina were Earhart, by clue 2, Dickey would be the council member who
had the 3-3 record and by elimination would be Helen--no (5). Gina had
the 3-3 voting record; Helen is Earhart. Ian is Dickey and Gina Angelico.
In sum, the five council members and their votes are as follows:
- John Bailey, 5 YES - 1 NO
- Helen Earhart, 4 YES - 2 NO
- Gina Angelico, 3 YES - 3 NO
- Ian Dickey, 2 YES - 4 NO
- Kathy Cohen, 1 YES - 5 NO
- Approve school budget, passed 5-0, YES: Bailey, Earhart, Angelico, Dickey, Cohen
- Hire new police chief, passed 4-1, YES: Bailey, Earhart, Angelico, Dickey; NO: Cohen
- Build central library, passed 3-2, YES: Bailey, Earhart, Angelico; NO: Dickey, Cohen
- Ban smoking in parks, defeated 2-3, YES: Bailey, Earhart; NO: Angelico, Dickey, Cohen
- Raise building height, defeated 1-4, YES: Bailey; NO: Earhart, Angelico, Dickey, Cohen
- Implement sales tax, defeated 0-5, NO: Bailey, Earhart; Angelico, Dickey, Cohen
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