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Problem of the Week 951

Upside Down LCD

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In an LCD display some numbers, when viewed upside-down, are images of other numbers. For example, 1995 becomes 5661. The fifth number that can be read upside down is 8, and the 15th is 21, which is 12 when viewed upside-down. What is the millionth number that is meaningful upside-down?

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NOTES
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An LCD numeral is obtained by filling in some of the 7 lines in the figure below.

 --
|  |
 --
|  |
 --

0: all but the central hyphen 1: The two right-hand verticals 8: All

2  --          3   --
     |               |
   --              --
  |                  |
   --              --


4             5   --
  |  |           |
   --             --
     |              |
                  --

6   --         7  --        9    --
   |                |           |  |
    --                           --
   |  |             |              |
    --                           --

Source: From the very nice new problem book, "50 Mathematical Puzzles and Problems; Red Collection", Key Curriculum Press, Gilles Cohen, ed., 2001, trans from French, Emeryville, Calif.

© Copyright 2002 Stan Wagon. Reproduced with permission.

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7 February 2002