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Rotational Years

Problem

If you write the year using the digits , the year was a special year because it read the same upside-down. How many years since the birth of Christ have had this property?


Solution

First we consider 1-digit and 2-digit years.

1-digit:1, 8
2-digit:11, 69, 88, 96

3-digit years include all 2-digit combinations with 0,1 and 8 in-between.

3-digit:101, 609, 808, 906
 111, 619, 818, 916
 181, 689, 888, 986

4-digit years are made of 1**1 with all 2-digit (including 00) combinations in-between.

4-digit:1001, 1111, 1691, 1881, 1961

So there are 23 years which have this property.

Which numbers under one million have this property?

Problem ID: 41 (Apr 2001)     Difficulty: 1 Star

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