The VOTE is in.....,.

[OldHen]

The Mayor Vote

Three people at odds with one another are running for mayor in the upcoming town election. 

Including these three candidates, the town has a voter population of 40 people.

In order to win, a candidate must get more votes than any other candidate.

If each of the 40 voters casts a single vote and every vote is recognized, what is the FEWEST number of votes a candidate needs to secure victory with a certainty?

[Crutch]

21

[letinmfly]

20

-If you take away the 3 candidates that leaves 37 other voters.
-The majority of the remaining 37 is 19.
-However one of the other candidates could vote for his opposition.
-Thus the winning candidate would need 20 votes to win.

[Boomstick]

they would need 14 votes,

40 total votes including candidates,
3 candidates so even would be 13 each
and that leaves 1 left over that would determine a winner.
so that makes 14 votes

[OldHen]

 

Answer: 20 Votes!
The winner has to have at least 20 votes for a certain victory. 
Since each of he candidates dislikes the other two, each will likely vote for themselves.  Forty votes minus those three leaves 37 votes.

The winner will need over HALF the remaining votes - in this case 19 additional votes.  Add the winning candidates OWN vote, and you get 20!

Even if another candidate gathered all remaining 18 votes, it wouldnt be enough to overcome the candidate with 20 votes.


20=1 +19     [candidate #1]
19=1 +18     [candidate #2]
1=1              [candidate #3]
___________
40 total votes

[Crutch]

20=1 +19     [candidate #1]
19=1 +18     [candidate #2]
1=1              [candidate #3]
___________
40 total votes

But
20=1 +19 candidate 1
19=1 +18 candidate 2
Candidate 3 votes for Candidate  2 to bringing total to 20.  Candidate 1 loses his certianty win and it is tied.

[OldHen]

20=1 +19     [candidate #1]
19=1 +18     [candidate #2]
1=1              [candidate #3]
___________
40 total votes

But
20=1 +19 candidate 1
19=1 +18 candidate 2
Candidate 3 votes for Candidate  2 to bringing total to 20.  Candidate 1 loses his certianty win and it is tied.

the dislike each other and would not vote for one another.... (see that at the question at that top ---had to make sure that was the case or otherwise you are right they could have been a tie....)

[Crutch]

tks, my bad.

[OldHen]

tks, my bad.

Nope its all good! LOL.... its an election...what do expect from politicians....those wankers!

[sugarray]

they would need 14 votes,

40 total votes including candidates,
3 candidates so even would be 13 each
and that leaves 1 left over that would determine a winner.
so that makes 14 votes

[OldHen]

they would need 14 votes,

40 total votes including candidates,
3 candidates so even would be 13 each
and that leaves 1 left over that would determine a winner.
so that makes 14 votes

Nope Ray...it was 20....

[OldHen]

haha read this thing 3 times before i could understand why the answer isnt 14.

I love brain teaser types... i will be looking for more....

[BOFF]

tks, my bad.

Nope its all good! LOL.... its an election...what do expect from politicians....those wankers!

I expect one of the politicians to buy the "likes" of himself from one of the the other candidates, and have a tie.  20-20

God Bless,
David B.