Professors O, P, Q, R, S, T, U, V, W, X, Y, and Z had lectures in different months of the same year: January, March, April, May, June, and December. E...

Professors O, P, Q, R, S, T, U, V, W, X, Y, and Z had lectures in different months of the same year: January, March, April, May, June, and December. Each lecture was held either on the 12th or 25th of these months, with no two professors lecturing on the same day. Each professor also prefers a unique color from Red, Blue, Green, Yellow, Orange, White, Pink, Silver, Maroon, Violet, Brown, and Grey.

Given the following clues:

• V lectured on 12th April.
• Exactly two people lectured between V and Q.
• The professor who likes Red lectured in the same month as Q, but Q does not like Red.
• The professor who likes White lectured on an even date in a month with 30 days; V does not like White.
• Exactly three people lectured between the professors who like White and Violet.
• The number of people between the professor who likes Red and O equals the number of people between Q and the professor who likes White.
• Exactly two people lectured between O and the professor who likes Blue.
• U lectured on the 12th of a month before the professor who likes Violet and does not like Red or Blue.
• Exactly two people lectured between U and the professor who likes Orange.
• Exactly two people lectured between the professors who like Orange and Green.
• X lectured in the same month as the professor who likes Green.
• The number of people lecturing after W equals the number lecturing before X.
• Exactly one person lectured between W and Z, with Z lecturing before W.
• The professor who likes Pink lectured on an odd date in the same month as Z.
• P lectured on the 12th of the same month as R.
• Exactly two people lectured between P and the professor who likes Yellow.
• The professor who likes Maroon lectured before P.
• T likes Brown.
• S does not like Red.
• W does not like Grey.

Question: How many people lectured between X and Y?