It is regarded as 120 point on the number axis, and Ak is used to indicate the group of 120 people who did not answer the K question correctly.

|Ak| is the number of people in this group, k=l, 2, 3, 4, 5,

Then |A 1|=24, |A2|=37, |A3|=46, |A4|=54, |A5|=85,

Give the above five groups five colors respectively,

If someone doesn't answer question k correctly,

This will mean that this person is recognized by K color, k = 1, 2, 3, 4, 5,

The question becomes, how many dots can you dye at least three colors at most?

Because | a1| +| a2 |+a3 |+| a4 |+| a5 | = 246,

So at least 2463=82 dots are dyed in three colors.

The upper right picture is the best dyeing method that meets the conditions.

That is, 85 points P 1, P2, …, P85 are dyed with the fifth color;

Points P 1, P2, …, P37 are dyed with the second color;

46 points P38, P39, …, P83 are dyed into the fourth color;

Dots P 1, P2, …, P24 are dyed with the first color;

54 points P25, P26, …, P78 are dyed in the third color;

So there are at most 78 dots dyed in three colors.

So there are at least 42 points with no more than two colors.

That is to say, there are at least 42 winners (each person answers at most two wrong questions and at least three right questions, such as P79, P80, …, P 120).

A: There are at least 42 winners.