Day Logic Puzzle Solution

The question asks us to identify a day that CANNOT be "the day before the day before yesterday" if the condition "the day after tomorrow is NOT Friday" is true.

Breaking Down the Timeline

Let's define "Today" as our reference point. We can express other days relative to Today:

• Tomorrow: Today + 1 day
• The day after tomorrow: Today + 2 days
• Yesterday: Today - 1 day
• The day before yesterday: Today - 2 days
• The day before the day before yesterday: Today - 3 days

So, the day we are interested in is equivalent to Today - 3 days.

Applying the Condition: Day After Tomorrow is NOT Friday

The condition is that "The day after tomorrow" is NOT Friday. This means "Today + 2 days" is NOT Friday.

If Today + 2 days is NOT Friday, it can be any other day of the week:

• Saturday
• Sunday
• Monday
• Tuesday
• Wednesday
• Thursday

Determining Possible "Today"s

Based on the possible values for "Today + 2 days", we can find the possible day for "Today". We subtract 2 days from each possibility:

• If Today + 2 days = Saturday, then Today = Saturday - 2 days = Thursday
• If Today + 2 days = Sunday, then Today = Sunday - 2 days = Friday
• If Today + 2 days = Monday, then Today = Monday - 2 days = Saturday
• If Today + 2 days = Tuesday, then Today = Tuesday - 2 days = Sunday
• If Today + 2 days = Wednesday, then Today = Wednesday - 2 days = Monday
• If Today + 2 days = Thursday, then Today = Thursday - 2 days = Tuesday

So, "Today" could be Thursday, Friday, Saturday, Sunday, Monday, or Tuesday.

Finding Possible Values for "Day Before the Day Before Yesterday"

Now, we need to find what day "The day before the day before yesterday" (which is Today - 3 days) would be for each of these possible "Today"s. We subtract 3 days from each possible "Today":

• If Today = Thursday, then Today - 3 days = Thursday - 3 days = Monday
• If Today = Friday, then Today - 3 days = Friday - 3 days = Tuesday
• If Today = Saturday, then Today - 3 days = Saturday - 3 days = Wednesday
• If Today = Sunday, then Today - 3 days = Sunday - 3 days = Thursday
• If Today = Monday, then Today - 3 days = Monday - 3 days = Friday
• If Today = Tuesday, then Today - 3 days = Tuesday - 3 days = Saturday

The possible days for "the day before the day before yesterday" are Monday, Tuesday, Wednesday, Thursday, Friday, and Saturday.

Identifying the Day That CANNOT Be

The question asks which of the given options CANNOT be the day before the day before yesterday. We compare our list of possible days (Monday, Tuesday, Wednesday, Thursday, Friday, Saturday) with the options:

1. Sunday
2. Monday
3. Tuesday
4. Wednesday

Looking at the options, Monday, Tuesday, and Wednesday are all in our list of possible days. Sunday is the only day in the options that is NOT in our list of possible days.

Therefore, if the day after tomorrow is NOT Friday, Sunday CANNOT be the day before the day before yesterday.