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The number must be evenly divisible by seven, since two dates that fall on the same day of the week must be separated by a number of days that is an integral multiple of seven. Notice that 18,263 = 2,6097, so this condition is satisfied. |
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The number of days must also represent an even number of years, so that the dates match for both month and day of the year. This condition can be satisfied in several ways, but there is a limited number of possibilities. |
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Every period of four years consists of three common years (CY) and one leap year (LY) arranged as: |
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Assuming that you do not stray over the border of a century and get involved with the complication of the 100-year leap year rule, this sequence represents what happens in the calendar. |
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Thus, no matter how many days intervene between two dates, the two dates are separated by some number of quads of 1,461 days, and some remaining number of days. Because quads can be treated as units, you can disregard them for the purpose of calculating the remainders, so you can look at the number of days, which can be a legitimate remainder between two dates, and still represent an integral number of years. This restriction cuts your choices down considerably, since you have a constant structure for the years within a quad and a fixed number of days within each year, and you are required to have a number of days that represents a complete year. This last consideration gives you a limited number of points in the quad where you can actually stop, no matter where you start. |
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In the following diagrams, S is a possible starting point, and  represents the only places that you can stop counting and |
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still keep an integral number of years and |
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stay within the confines of one quad. |
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The four diagrams represent all of the possible cases. |
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