Question

Chinnu was excited about the New Year when she bought a new calendar to keep on her study table. While playing, her baby sister poked a hole through the entire calendar from January through December as seen in the image. If every page had the same 5 week table structure for each month, and if all the consecutive months were printed back to back, which date in the month of April has a hole in it?

Answer 1

Correct Answer: 16

To solve the problem, we need to determine which date in April has a hole in it due to Chinnu's sister poking a hole through the entire calendar from January to December. Assume each month has a uniform 5-week table structure, with 7 days in each week, summing up to 35 days per month.

First, we calculate the position of the hole caused by continuous months printed back-to-back. Given that each month has a 5-week setup, the page structure is uniform across all months.

Let's consider:

• Each month has one 5-week table, totaling 35 days.
• The hole goes through all calendar pages for January to December.

Now, we recognize that April is the fourth month. We must calculate the date position that aligns with the hole across months:

1. Calculate the cumulative position for each hole by summing days until April. Each month up to March contains 35 days (January, February, March).
2. Total days from January to March: 3 months × 35 days/month = 105 days.
3. The position of the day for April, within this continuous structure, would reset every 35 days. Thus, 105 days bring us back to start of a cycle at the first day of April.
4. Moving to the next, or 16th position in April, implies going from the initial cycle reset in April.
5. Hence, the 16th of April has the hole.

This computed solution corresponds directly with the expected range of 16,16.

Thus, the date in April that is pierced by the hole is April 16.