As of the date this question was asked, August 12, 2010, the date 81 days from this day will be November 1, 2010.
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To solve the riddle, we start from "the day after the day after tomorrow," which is two days from today. If that day is four days before Monday, then two days from today is Sunday (since four days before Monday is Thursday). Therefore, today is Friday.
If today is Wednesday it will be Saturday 136 days (19 weeks and 3 days) from today.
Friday
Tuesday
274 : 7 = 39.1.... 274 - 7 * 39 = 1, so, in 274 days there will be the next day after the day like today. For example, if today is Sunday, in 274 days there will be Monday.