Alice, Bob, Candice and David run for school president. There are 201 students in the school and each student can vote for only one candidate. The person with the largest number of votes is the winner. If every student votes, what is the minimum number of votes needed to win the election?

The minimum number to win could be 51, if other students got a tie at 50,50,50. However, getting 51 does not guarantee a win. The minimum number to win guaranteed, not dependent on the others votes, is 101 votes. With 101 votes, no other person can win.

To find the minimum number of votes needed to win the election, we need to determine the number of votes received by each candidate.

Since there are 201 students in the school and each student can vote for only one candidate, the total number of votes cast in the election will be 201.

To find the minimum number of votes needed to win, we need to consider the scenario where one candidate receives the majority of votes. In this case, the remaining candidates would receive fewer votes than the winner.

Let's calculate the minimum number of votes required for a candidate to win:

1. Assuming the candidate with the majority of votes received x votes, the remaining candidates would need to receive fewer votes.

2. The remaining three candidates (Alice, Bob, and Candice) must receive fewer votes than the winner. Therefore, their combined votes should be less than x.

3. David, being one of the candidates, would also need to receive fewer votes than the winner. Therefore, his votes should be less than x as well.

4. Since every student votes, the total number of votes for Alice, Bob, Candice, and David should add up to 201.

To find the minimum number of votes needed to win, let's start with the assumption that one candidate receives 101 votes, which is exactly half of the total votes cast:

- For Alice, Bob, and Candice combined, there will be 201 - 101 = 100 votes.
- For David, the votes will be less than 101.

Since the candidate with the majority of votes will have 101 votes, the minimum number of votes needed to win the election is 101.

To find the minimum number of votes needed to win the election, we need to determine the maximum possible number of votes each candidate can receive. Since there are 201 students in the school, and each student can vote for only one candidate, the maximum number of votes a candidate can receive is 201.

However, we need to consider that there are four candidates running for president: Alice, Bob, Candice, and David. Therefore, we need to divide the total number of votes (201) by the number of candidates (4) to determine the minimum number of votes needed to win the election.

The minimum number of votes needed to win the election is 201 divided by 4, which equals 50.25.

Since we cannot have a fractional number of votes, we round up the minimum number of votes to the nearest whole number. Therefore, the minimum number of votes needed to win the election is 51.