Steve is in charge of designing a wall-hanging calendar. Each month is allocated a grid of 5 X 7 squares, labeled Sunday thru Saturday across the top. The problem is, Steve hates to put two dates in the same square on the calendar, necessary when the month spans parts of six weeks. Is it possible for Steve to find a year when he never has to put two dates in the same square? What is the most double-date squares he would ever need for a single year?

(In reply to Pesky months by Bob Smith)

A leap year beginning on a Saturday has 4 double-date months.

Also, while you could double up the first day, rather than the last two, for a 31-day month starting on a Saturday, in practice calendar makers double up on the last two.  But if Steve hates these double dates so much, maybe he'd depart from the usual practice.  Then the most he'd need to put in any year is the 4 maximum months that require double-dates, as only one double-date would be needed in any month.

Posted by Charlie on 2005-09-14 14:02:22