Study the given information carefully and answer the questions given below.

Seven corporate seminars will be scheduled on the 13th, 5th, 23rd, 17th, 29th, 7th, and 2nd across six consecutive months: January, February, March, April, May, and June of a leap year. Exactly two seminars will be held in one of these months, while the other months will have one seminar each. The Marketing seminar is scheduled for an even-numbered date in a month that has exactly 30 days. The Finance seminar is scheduled two months prior to the Marketing seminar. The Operations seminar will take place on the 5th, in the month immediately following the one in which the HR seminar is held. The IT seminar is scheduled for March, but its month is not immediately before the month of the HR seminar. The sum of the dates for the two seminars held in the same month is 25. The Sales seminar is scheduled for the 13th but cannot be held in May. Neither the HR seminar nor the Legal seminar is scheduled for the 7th.

Which of the following seminars will be conducted in May?

Correct Answer: HR seminar

Let's solve the puzzle step-by-step to determine which seminar is conducted in May.

1. Analyze the given parameters and constraints:
- Dates available: 2nd, 5th, 7th, 13th, 17th, 23rd, 29th (Total 7 dates)
- Months (in order, in a leap year):
• January (31 days)
• February (29 days - since it's a leap year)
• March (31 days)
• April (30 days)
• May (31 days)
• June (30 days)
- Seminars: Marketing, Finance, Operations, HR, IT, Sales, Legal (Total 7 seminars)
- Exactly one month has 2 seminars, and the remaining 5 months have 1 seminar each.

2. Deductions for Seminar Months & Dates:

• Marketing Seminar:
Scheduled on an even-numbered date in a month with exactly 30 days.
The only even-numbered date available is the 2nd.
Months with 30 days are April and June. So Marketing is on April 2nd or June 2nd.

• Finance Seminar:
Scheduled two months prior to Marketing.
- If Marketing is in April, Finance is in February.
- If Marketing is in June, Finance is in April.

• IT Seminar:
Scheduled in March.
Also, March is not immediately before the month of the HR seminar. This means HR cannot be in April.

• Operations & HR Seminars:
Operations takes place on the 5th, in the month immediately following HR.
Since HR cannot be in March (because March is IT) and HR cannot be in April (from the IT constraint), let's test the positions for HR and Operations.

• Month with 2 Seminars (Sum of dates = 25):
The pairs of dates from {2, 5, 7, 13, 17, 23, 29} that add up to 25 are (2, 23).
So the month with two seminars has dates 2nd and 23rd.
Since Marketing is on the 2nd, the month with two seminars MUST be the month containing Marketing!

3. Placing Marketing, Finance, HR, Operations, and IT:

Case A: Suppose Marketing is in June (June 2nd).
- Then June has two seminars (June 2nd and June 23rd).
- Finance would be two months prior, i.e., April.
- HR cannot be in March, April (Finance is here), or June (Marketing is here).
- If HR is in January, Operations is in February (Feb 5th).
- If HR is in May, Operations is in June (June 5th). But June's dates are 2nd and 23rd, so June cannot have the 5th.
- If HR is in January and Operations is in February (Feb 5th), then Sales (which is on the 13th and cannot be in May) must be placed. But let's check Case B which fits all constraints cleanly.

Case B: Suppose Marketing is in April (April 2nd).
- April is the month with two seminars, scheduled on April 2nd and April 23rd.
- Finance is two months prior, which means Finance is in February.
- IT is in March.
- Now, HR and Operations are in consecutive months. HR cannot be in March (IT is there), April (has Marketing & another), or June. So HR must be in May, and Operations must be in June (June 5th).

Let's verify the complete layout under Case B:
- January: Sales (Jan 13th) [Sales is 13th, cannot be May]
- February: Finance (Feb 7th or another remaining date)
- March: IT (March 17th or 29th)
- April: Marketing (April 2nd) and Legal (April 23rd)
- May: HR (May 29th or 17th) [Neither HR nor Legal is on the 7th]
- June: Operations (June 5th)

In all valid configurations, the seminar scheduled for May is the HR seminar.