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To: E. Charters who wrote (80440)1/2/2002 1:05:53 AM
From: Don Lloyd  Read Replies (1) | Respond to of 116753
 
EC -

Yes, but did you know that 2002 is a symmetrical year, evenly divisible by 11? Like 1991 last and 2112 next? Are all 4 digit symmetrical years divisible by 11?

Yes.

All 4 digit symmetrical decimal numbers have the form abba, where a can be 1 to 9 and b can be 0 to 9.

Starting with the maximum possible symmetrical 4 digit number, 9999, it can be factored into 11 X 909.

Every other possible 4 digit symmetrical number can be generated from 9999 by subtracting either 110 (11X10) or 1001 (11X91) or a combination of both an integral number of times each.

Thus any 4 digit symmetrical number can be formed as ( 9999 - m X 110 - n X 1001 ), where m and n are integers such that the overall result is greater than 1000, and the overall result can be evenly divided by 11 to give ---
(909 - 10m - 91n).

Regards, Don