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Double Dates (Posted on 2005-09-14) Difficulty: 2 of 5
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?

See The Solution Submitted by Josh70679    
Rating: 3.3333 (3 votes)

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Solution re(2): Pesky months -- alternative count Comment 4 of 4 |
(In reply to re: Pesky months by Charlie)

If we count each month that requires a double date as requiring only one double date (doubling up at the beginning of the month if necessary to avoid two double date boxes in a month), the table becomes:

Su31  We28  We31  Sa30* Mo31  Th30  Sa31* Tu31  Fr30  Su31  We30  Fr31*  3
Mo31  Th28  Th31  Su30  Tu31  Fr30  Su31  We31  Sa30* Mo31  Th30  Sa31*  2
Tu31  Fr28  Fr31* Mo30  We31  Sa30* Mo31  Th31  Su30  Tu31  Fr30  Su31   2
We31  Sa28  Sa31* Tu30  Th31  Su30  Tu31  Fr31* Mo30  We31  Sa30* Mo31   3
Th31  Su28  Su31  We30  Fr31* Mo30  We31  Sa31* Tu30  Th31  Su30  Tu31   2
Fr31* Mo28  Mo31  Th30  Sa31* Tu30  Th31  Su31  We30  Fr31* Mo30  We31   3
Sa31* Tu28  Tu31  Fr30  Su31  We30  Fr31* Mo31  Th30  Sa31* Tu30  Th31   3
Su31  We29  Th31  Su30  Tu31  Fr30  Su31  We31  Sa30* Mo31  Th30  Sa31*  2
Mo31  Th29  Fr31* Mo30  We31  Sa30* Mo31  Th31  Su30  Tu31  Fr30  Su31   2
Tu31  Fr29  Sa31* Tu30  Th31  Su30  Tu31  Fr31* Mo30  We31  Sa30* Mo31   3
We31  Sa29  Su31  We30  Fr31* Mo30  We31  Sa31* Tu30  Th31  Su30  Tu31   2
Th31  Su29  Mo31  Th30  Sa31* Tu30  Th31  Su31  We30  Fr31* Mo30  We31   2
Fr31* Mo29  Tu31  Fr30  Su31  We30  Fr31* Mo31  Th30  Sa31* Tu30  Th31   3
Sa31* Tu29  We31  Sa30* Mo31  Th30  Sa31* Tu31  Fr30  Su31  We30  Fr31*  4

with a minimum of 2 and a maximum of 4 double dates in the year.


  Posted by Charlie on 2005-09-14 14:07:39
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